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Garis l adalah garis singgung sekutu parabola y = x2 − 4x + 7 dan y = p − 3(x + 2)2. Jika garis l menyinggung parabola y = x2 − 4x + 7 di x = 5 maka p = ….

Pertanyaan

Garis l adalah garis singgung sekutu parabola y = x2 − 4x + 7 dan y = p − 3(x + 2)2. Jika garis l menyinggung parabola y = x2 − 4x + 7 di x = 5 maka p = ….
 

  1. −35

  2. −33

  3. −26

  4. −21

  5. −10

Pembahasan Soal:

Garis space straight l space menyinggung space parabola space straight y equals straight x squared minus 4 straight x plus 7 space di space straight x equals 5 comma space maka space garis  tersebut space memiliki space gradien  straight m equals straight y apostrophe equals 2 straight x minus 4 equals 2 left parenthesis 5 right parenthesis minus 4 equals 10 minus 4 equals box enclose 6    Titik space singgungnya space diketahui space pada space saat space box enclose straight x equals 5 end enclose comma space sehingga  straight y equals left parenthesis 5 right parenthesis squared minus 4 left parenthesis 5 right parenthesis plus 7 equals 25 minus 20 plus 7 equals box enclose 12  Sehingga space straight l space memiliki space gradien space box enclose straight m equals 6 end enclose space dan space melalui space titik space box enclose left parenthesis 5 comma 12 right parenthesis end enclose.  Persamaan space garis space straight l space adalah  straight y minus straight y subscript 1 equals straight m open parentheses straight x minus straight x subscript 1 close parentheses  straight y minus 12 equals 6 open parentheses straight x minus 5 close parentheses  straight y minus 12 equals 6 straight x minus 30  box enclose straight y equals 6 straight x minus 18 end enclose    Garis space straight l space menyinggung space parabola space straight y equals straight p minus 3 open parentheses straight x plus 2 close parentheses squared.  straight y subscript garis equals straight y subscript parabola  6 straight x minus 18 equals straight p minus 3 open parentheses straight x plus 2 close parentheses squared  3 open parentheses straight x plus 2 close parentheses squared plus 6 straight x minus 18 minus straight p equals 0  3 open parentheses straight x squared plus 4 straight x plus 4 close parentheses plus 6 straight x minus 18 minus straight p equals 0  3 straight x squared plus 12 straight x plus 12 plus 6 straight x minus 18 minus straight p equals 0  3 straight x squared plus 18 straight x minus 6 minus straight p equals 0    Karena space garis space dan space parabola space bersinggungan comma space maka  straight D equals 0  left parenthesis 18 right parenthesis squared minus 4 left parenthesis 3 right parenthesis left parenthesis negative 6 minus straight p right parenthesis equals 0  324 plus 72 plus 12 straight p equals 0  396 plus 12 straight p equals 0  12 straight p equals negative 396  box enclose straight p equals negative 33 end enclose

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rizky

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 17 Desember 2020

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Pertanyaan yang serupa

Tentukan persamaan garis singgung dengan grafiknya dari y=x3−2x2+6 pada titik (2,4).

Pembahasan Soal:

Diketahui grafik fungsi begin mathsize 14px style y equals x cubed minus 2 x squared plus 6 end style. Untuk mencari persamaan garis singgung dibutuhkan informasi nilai gradien dan titik yang dilaluinya. Gradien dapat dicari dengan menggunakan turunan pertama dari fungsi. Turunan pertama dari fungsi begin mathsize 14px style y end style diperoleh sebagai berikut.

begin mathsize 14px style y apostrophe equals 3 x squared minus 4 x end style 

Akibatnya gradien garis singgung fungsi tersebut pada titik begin mathsize 14px style left parenthesis 2 comma space 4 right parenthesis end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row m equals cell y apostrophe end cell row blank equals cell 3 left parenthesis 2 squared right parenthesis minus 4 left parenthesis 2 right parenthesis end cell row blank equals cell 12 minus 8 end cell row blank equals 4 end table end style 

Ingat bahwa persamaan garis yang melaui titik (x1,y1) dengan gradien begin mathsize 14px style m end style diberikan sebagai berikut.

begin mathsize 14px style y minus y subscript 1 equals m open parentheses x minus x subscript 1 close parentheses end style 

Dengan demikian, persamaan garis singgung grafik fungsi begin mathsize 14px style y equals x cubed minus 2 x squared plus 6 end style pada titik (2,4) diperoleh sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m open parentheses x minus x subscript 1 close parentheses end cell row cell y minus 4 end cell equals cell 4 open parentheses x minus 2 close parentheses end cell row cell y minus 4 end cell equals cell 4 x minus 8 end cell row y equals cell 4 x minus 4 end cell end table end style 

Jadi, persamaan garis singgung dengan grafik begin mathsize 14px style y equals x cubed minus 2 x squared plus 6 end style pada titik begin mathsize 14px style left parenthesis 2 comma space 4 right parenthesis end style adalah y=4x4.

0

Roboguru

Persamaan garis singgung grafik y=−4x+xx​ yang sejajar dengan garis 5x+2y+4=0 adalah ...

Pembahasan Soal:

Pertama kita cari turunan pertama dari y equals negative 4 x plus x square root of x 

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 4 x plus x square root of x end cell row y equals cell negative 4 x plus x to the power of 3 over 2 end exponent end cell row cell y apostrophe end cell equals cell negative 4 plus 3 over 2 open parentheses x close parentheses to the power of 1 half end exponent end cell row cell y apostrophe end cell equals cell negative 4 plus 3 over 2 square root of x end cell row blank blank blank end table 

Misalnya gradien dari garis singgung grafik tersebut adalah straight m subscript 2
Karena gradien garis singgung grafik merupakan turunan pertama dari fungsi grafinya maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m subscript 1 end cell equals cell straight y apostrophe end cell row cell straight m subscript 1 end cell equals cell negative 4 plus 3 over 2 square root of straight x end cell end table 

Misalnya gradien garis 5 x plus 2 y plus 4 equals 0 adalah straight m subscript 2, maka 

straight m subscript 2 equals negative fraction numerator koefisien space straight x over denominator koefisien space straight y end fraction straight m subscript 2 equals negative 5 over 2 

Karena sejajar, maka gradien kedua garis sama. Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m subscript 1 end cell equals cell straight m subscript 2 end cell row cell negative 4 plus 3 over 2 square root of x end cell equals cell negative 5 over 2 end cell row cell 3 over 2 square root of x end cell equals cell negative 5 over 2 plus 4 end cell row cell 3 over 2 square root of x end cell equals cell 3 over 2 end cell row cell square root of x end cell equals 1 row x equals 1 end table 

Substitusi nilai x equals 1 ke y equals negative 4 x plus x square root of x diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell negative 4 open parentheses 1 close parentheses plus open parentheses 1 close parentheses square root of 1 end cell row blank equals cell negative 4 plus 1 end cell row blank equals cell negative 3 end cell end table 

Jadi titik singgunganya adalah open parentheses 1 comma space minus 3 close parentheses dengan gradien straight m subscript 1 equals straight m subscript 2 equals negative 5 over 2. Sehingga persamaan garis singgungnya adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell straight m subscript 1 open parentheses x minus x subscript 1 close parentheses end cell row cell y minus open parentheses negative 3 close parentheses end cell equals cell open parentheses negative 5 over 2 close parentheses open parentheses x minus 1 close parentheses end cell row cell y plus 3 end cell equals cell negative 5 over 2 x plus 5 over 2 end cell row cell 2 y plus 6 end cell equals cell negative 5 x plus 5 end cell row cell 5 x plus 2 y end cell equals cell negative 1 end cell end table 

Jadi persamaan garis singgung grafik tersebut adalah 5 x plus 2 y equals negative 1

0

Roboguru

Tentukan persamaan garis singgung dan persamaan garis normal di titik dengan absis x=1 pada setiap fungsi berikut. Petunjuk: carilah gradien persamaan garis singgung dengan menggunakan limit fungsi. ...

Pembahasan Soal:

Gradien garis singgung suatu kurva begin mathsize 14px style f left parenthesis x right parenthesis end style didefinisikan oleh

begin mathsize 14px style m subscript g s end subscript equals f apostrophe open parentheses a close parentheses equals limit as h rightwards arrow 0 of fraction numerator f open parentheses a plus h close parentheses minus f open parentheses a close parentheses over denominator h end fraction end style.

dengan begin mathsize 14px style open parentheses a comma space b close parentheses end style adalah koordinat titik singgungnya.

Maka gradien garis singgung kurva begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x squared end style di titik dengan absis begin mathsize 14px style x equals 1 end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript end cell equals cell f apostrophe left parenthesis 1 right parenthesis end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis 1 plus h right parenthesis minus f left parenthesis 1 right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style 2 open parentheses 1 plus h close parentheses squared minus 2 open parentheses 1 close parentheses squared end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style 2 open parentheses 1 plus 2 h plus h squared close parentheses minus 2 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style 2 plus 4 h plus 2 h squared minus 2 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 4 h plus 2 h squared over denominator h end fraction times end cell row blank equals cell limit as h rightwards arrow 0 of open parentheses 4 plus 2 h close parentheses end cell row blank equals cell 4 plus 0 end cell row blank equals 4 end table end style

Selanjutnya, kita akan menghitung ordinat titik singgungnya. Substitusikan begin mathsize 14px style x equals 1 end style ke persamaan kurva begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x squared end style sehingga diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f left parenthesis 1 right parenthesis end cell row blank equals cell 2 open parentheses 1 close parentheses squared end cell row blank equals 2 end table end style

Dengan demikian, persamaan garis singgungnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g s end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 2 end cell equals cell 4 left parenthesis x minus 1 right parenthesis end cell row cell y minus 2 end cell equals cell 4 x plus 4 end cell row cell y minus 4 x minus 6 end cell equals 0 end table end style

Selanjutnya, karena garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis end style saling berpotongan tegak lurus di titik singgung begin mathsize 14px style open parentheses a comma space b close parentheses end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript times m subscript g n end subscript end cell equals cell negative 1 end cell row cell 4 times m subscript g n end subscript end cell equals cell negative 1 end cell row cell m subscript g n end subscript end cell equals cell negative 1 fourth end cell end table end style

dan persamaan garis normalnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g n end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 2 end cell equals cell negative 1 fourth left parenthesis x minus 1 right parenthesis end cell row cell y minus 2 end cell equals cell negative 1 fourth x plus 1 fourth end cell row cell 4 y minus 8 end cell equals cell negative x plus 1 end cell row cell 4 y plus x minus 9 end cell equals 0 end table end style

Jadi, persamaan garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x squared end style pada titik dengan absis begin mathsize 14px style x equals 1 end style dan ordinat begin mathsize 14px style y equals 2 end style berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 9 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table.

1

Roboguru

Tentukan persamaan garis singgung dan persamaan garis normal di titik dengan absis x=1 pada setiap fungsi berikut. Petunjuk: carilah gradien persamaan garis singgung dengan menggunakan limit fungsi. ...

Pembahasan Soal:

Gradien garis singgung suatu kurva begin mathsize 14px style f left parenthesis x right parenthesis end style didefinisikan oleh

begin mathsize 14px style m subscript g s end subscript equals f apostrophe open parentheses a close parentheses equals limit as h rightwards arrow 0 of fraction numerator f open parentheses a plus h close parentheses minus f open parentheses a close parentheses over denominator h end fraction end style.

dengan begin mathsize 14px style open parentheses a comma space b close parentheses end style adalah koordinat titik singgungnya.

Maka gradien garis singgung kurva begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 over denominator x plus 1 end fraction end style di titik dengan absis begin mathsize 14px style x equals 1 end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript end cell equals cell f apostrophe left parenthesis 1 right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis 1 plus h right parenthesis minus f left parenthesis 1 right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style 2 over open parentheses 2 plus h close parentheses squared minus 2 over open parentheses 2 close parentheses squared end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator 2 over denominator 4 plus 4 h plus h squared end fraction minus 2 over 4 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator 2 over denominator 4 plus 4 h plus h squared end fraction minus 1 half end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator 4 minus open parentheses 4 plus 4 h plus h squared close parentheses over denominator 8 plus 8 h plus 2 h squared end fraction end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left parenthesis 4 minus 4 minus 4 h minus h squared right parenthesis over denominator 8 plus 8 h plus 2 h squared end fraction times 1 over h end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left parenthesis negative 4 h minus h squared right parenthesis over denominator 8 plus 8 h plus 2 h squared end fraction times 1 over h end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left parenthesis negative 4 minus h right parenthesis up diagonal strike h to the power of 1 over denominator 8 plus 8 h plus 2 h squared end fraction times 1 over up diagonal strike h to the power of 1 end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative 4 minus 2 h over denominator 8 plus 8 h plus 2 h squared end fraction end cell row blank equals cell fraction numerator negative 4 minus 0 over denominator 8 plus 0 plus 0 end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 8 end fraction end cell row blank equals cell negative 1 half end cell end table end style

Selanjutnya, kita akan menghitung ordinat titik singgungnya. Substitusikan begin mathsize 14px style x equals 1 end style ke persamaan kurva begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 over denominator x plus 1 end fraction end style sehingga diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f left parenthesis 1 right parenthesis end cell row blank equals cell fraction numerator 2 over denominator 1 plus 1 end fraction end cell row blank equals cell 2 over 2 end cell row blank equals 1 end table end style

Dengan demikian, persamaan garis singgungnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g s end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 1 end cell equals cell negative 1 half left parenthesis x minus 1 right parenthesis end cell row cell 2 y minus 2 end cell equals cell negative open parentheses x minus 1 close parentheses end cell row cell 2 y minus 2 plus open parentheses x minus 1 close parentheses end cell equals 0 row cell 2 y plus x minus 3 end cell equals 0 end table end style

Selanjutnya, karena garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis end style saling berpotongan tegak lurus di titik singgung begin mathsize 14px style open parentheses a comma space b close parentheses end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript times m subscript g n end subscript end cell equals cell negative 1 end cell row cell negative 1 half times m subscript g n end subscript end cell equals cell negative 1 end cell row cell m subscript g n end subscript end cell equals 2 end table end style

dan persamaan garis normalnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g n end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 1 end cell equals cell 2 left parenthesis x minus 1 right parenthesis end cell row cell y minus 1 end cell equals cell 2 x minus 2 end cell row cell y minus 2 x minus 1 plus 2 end cell equals 0 row cell y minus 2 x plus 1 end cell equals 0 end table end style

Jadi, persamaan garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 over denominator x plus 1 end fraction end style pada titik dengan absis begin mathsize 14px style x equals 1 end style dan ordinat size 14px y size 14px equals size 14px 1berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table.

0

Roboguru

Tentukan persamaan garis singgung dan persamaan garis normal di titik dengan absis x=1 pada setiap fungsi berikut. Petunjuk: carilah gradien persamaan garis singgung dengan menggunakan limit fungsi. ...

Pembahasan Soal:

Gradien garis singgung suatu kurva begin mathsize 14px style f left parenthesis x right parenthesis end style didefinisikan sebagai berikut.

begin mathsize 14px style m subscript g s end subscript equals f apostrophe open parentheses a close parentheses equals limit as h rightwards arrow 0 of fraction numerator f open parentheses a plus h close parentheses minus f open parentheses a close parentheses over denominator h end fraction end style.

 begin mathsize 14px style open parentheses a comma space b close parentheses end style adalah koordinat titik singgungnya.

Berdasarkan rumus di atas, diperoleh gradien garis singgung kurva begin mathsize 14px style f left parenthesis x right parenthesis equals open parentheses 2 x minus 1 close parentheses cubed end style di titik dengan absis begin mathsize 14px style x equals 1 end style sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript end cell equals cell f apostrophe open parentheses 1 close parentheses end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator f open parentheses 1 plus h close parentheses minus f open parentheses 1 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style open parentheses 2 open parentheses 1 plus h close parentheses minus 1 close parentheses cubed minus open parentheses 2 open parentheses 1 close parentheses minus 1 close parentheses cubed end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style open parentheses 2 plus 2 h minus 1 close parentheses cubed minus 1 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style open parentheses 2 h plus 1 close parentheses cubed minus 1 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style 8 h cubed plus 12 h squared plus 6 h plus 1 minus 1 end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 8 h cubed plus 12 h squared plus 6 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator left parenthesis 8 h squared plus 12 h plus 6 right parenthesis up diagonal strike h to the power of 1 over denominator up diagonal strike h to the power of 1 end fraction end cell row blank equals cell limit as h rightwards arrow 0 of left parenthesis 8 h squared plus 12 h plus 6 right parenthesis end cell row blank equals cell 0 minus 0 plus 6 end cell row blank equals 6 end table

Selanjutnya, kita akan menghitung ordinat titik singgungnya. Substitusikan begin mathsize 14px style x equals 1 end style ke persamaan kurva begin mathsize 14px style f left parenthesis x right parenthesis equals open parentheses 2 x minus 1 close parentheses cubed end style sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f left parenthesis 1 right parenthesis end cell row blank equals cell open parentheses 2 open parentheses 1 close parentheses minus 1 close parentheses cubed end cell row blank equals 1 end table end style

Dengan demikian, persamaan garis singgungnya adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g s end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 1 end cell equals cell 6 left parenthesis x minus 1 right parenthesis end cell row cell y minus 1 end cell equals cell 6 x minus 6 end cell row cell y minus 6 x plus 5 end cell equals 0 end table end style

Selanjutnya, dikarenakan garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis end style saling berpotongan tegak lurus di titik singgung begin mathsize 14px style open parentheses a comma space b close parentheses end style, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript g s end subscript times m subscript g n end subscript end cell equals cell negative 1 end cell row cell 6 times m subscript g n end subscript end cell equals cell negative 1 end cell row cell m subscript g n end subscript end cell equals cell negative 1 over 6 end cell end table end style

Kemudian, diperoleh persamaan garis normalnya sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m subscript g n end subscript left parenthesis x minus a right parenthesis end cell row cell y minus 1 end cell equals cell negative 1 over 6 left parenthesis x minus 1 right parenthesis end cell row cell 6 y minus 6 end cell equals cell negative open parentheses x minus 1 close parentheses end cell row cell 6 y minus 6 plus open parentheses x minus 1 close parentheses end cell equals 0 row cell 6 y plus x minus 7 end cell equals 0 end table end style

Dengan demikian, persamaan garis singgung dan garis normal kurva begin mathsize 14px style f left parenthesis x right parenthesis equals open parentheses 2 x minus 1 close parentheses cubed end style pada titik dengan absis begin mathsize 14px style x equals 1 end style dan ordinat undefined berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 0 end table.

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Roboguru

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