Roboguru

Persamaan garis normal pada kurva y=x​+x​1​+xx​1​  di titik (1, 3) adalah ....

Pertanyaan

Persamaan garis normal pada kurva y=x+x1+xx1  di titik (1, 3) adalah ....

  1. begin mathsize 14px style 3 x plus 2 y minus 9 equals 0 end style 

  2. size 14px 3 size 14px x size 14px minus size 14px 2 size 14px y size 14px plus size 14px 3 size 14px equals size 14px 0 

  3. size 14px 2 size 14px x size 14px minus size 14px 3 size 14px y size 14px plus size 14px 3 size 14px equals size 14px 0  

  4. size 14px 2 size 14px x size 14px minus size 14px 3 size 14px y size 14px plus size 14px 7 size 14px equals size 14px 0 

  5. size 14px 2 size 14px x size 14px minus size 14px 3 size 14px y size 14px plus size 14px 9 size 14px equals size 14px 0 

Pembahasan Soal:

Garis normal merupakan garis yang melalui titik singgung dan tegak lurus dengan garis singgung. 

Dua garis tegak lurus jika perkalian gradiennya adalah 1, sehingga:

m1m2=1m2=m11 

Secara umum, persamaan garis normal bergradien m11 dan melalui titik A(x1,y1) yaitu:

yy1=m11(xx1) 

Terlebih dahulu kita cari gradien (m) dari y=x+x1+xx1 yaitu:

m1yyym1========yx+x1+xx1x21+x21+x2321x21121x21123x23121x2121x2323x2521x2xx12x2x3,substitusix=121212323 

Sehingga, persamaan garis normal pada kurva y=x+x1+xx1  di titik (1, 3) diperoleh:

yy1y3y33(y3)3y92x+3y9+22x+3y72x3y+7========m11(xx1)231(x1)32(x1)2(x1)2x2000 

Dengan demikian, garis normalnya yaitu 2x3y+7=0.

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Tessalonika

Mahasiswa/Alumni Universitas Negeri Medan

Terakhir diupdate 30 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

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

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 open parentheses x close parentheses equals 2 x 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 minus 2 open parentheses 1 close parentheses 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 h end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 2 end cell row blank equals 2 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 open parentheses x close parentheses equals 2 x 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 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 2 left parenthesis x minus 1 right parenthesis end cell row cell y minus 2 end cell equals cell 2 x minus 2 end cell row y equals cell 2 x end cell 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 2 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 half 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 half left parenthesis x minus 1 right parenthesis end cell row cell y minus 2 end cell equals cell negative 1 half x plus 1 half end cell row y equals cell negative 1 half x plus 5 over 2 end cell end table end style

Jadi, persamaan garis singgung dan garis normal kurva begin mathsize 14px style f open parentheses x close parentheses equals 2 x 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 size 14px equals blank 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 (kurva itu sendiri) dan begin mathsize 14px style y equals negative 1 half x plus 5 over 2 end style.

Roboguru

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

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.

Roboguru

Persamaan garis singgung grafik  yang sejajar dengan garis  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

Roboguru

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

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.

Roboguru

Garis singgung pada parabola  yang sejajar dengan garis  adalah ...

Pembahasan Soal:

Diketahui:

begin mathsize 14px style y equals x squared plus 6 1 half x plus 14 1 half end style
begin mathsize 14px style x minus 2 y plus 3 equals 0 end style

Mencari gradien:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x – 2 y plus 3 end cell equals cell 0 rightwards arrow straight a equals 1 comma straight b equals – 2 comma straight c equals 3 end cell row straight m equals cell – straight a over straight b end cell row straight m equals cell – fraction numerator 1 over denominator negative 2 end fraction end cell row straight m equals cell 1 half end cell end table end style  

Karena garis sejajar, maka begin mathsize 14px style straight m subscript 1 equals straight m subscript 2 equals 1 half end style.

Mencari titik singgung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus open parentheses 6 1 half close parentheses x plus 14 1 half end cell row cell y ’ end cell equals cell 2 x plus 13 over 2 end cell row cell y ’ end cell equals cell straight m subscript 2 end cell row cell 2 x plus 13 over 2 end cell equals cell 1 half end cell row cell 2 x end cell equals cell 1 half – 13 over 2 end cell row cell 2 x end cell equals cell – 12 over 2 end cell row cell 2 x end cell equals cell – 6 end cell row x equals cell – 3 end cell end table end style 

Substitusi begin mathsize 14px style x equals – 3 end style pada persamaan garis singgung kurva:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus open parentheses 6 1 half close parentheses x plus 14 1 half end cell row y equals cell open parentheses negative 3 close parentheses squared plus open parentheses 6 1 half close parentheses open parentheses negative 3 close parentheses plus 14 1 half end cell row y equals cell 9 plus 13 over 2 open parentheses negative 3 close parentheses plus 29 over 2 end cell row y equals cell 9 – open parentheses 39 over 2 close parentheses plus 29 over 2 blank end cell row y equals cell 9 – 10 over 2 blank end cell row y equals cell 9 – 5 end cell row y equals 4 end table end style 

Diperoleh titik singgung begin mathsize 14px style open parentheses negative 3 comma space 4 close parentheses end style.

Didapat persamaan garis singgung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses – 3 , space 4 close parentheses end cell rightwards arrow cell open parentheses x subscript 1 comma space y subscript 1 close parentheses end cell row cell y – y subscript 1 end cell equals cell straight m subscript 2 open parentheses x – x subscript 1 close parentheses end cell row cell y – 4 end cell equals cell 1 half open parentheses x – open parentheses negative 3 close parentheses close parentheses end cell row cell y – 4 end cell equals cell 1 half open parentheses x plus 3 close parentheses end cell row cell 2 open parentheses y – 4 close parentheses end cell equals cell x plus 3 end cell row cell 2 y – 8 end cell equals cell x plus 3 end cell row cell 2 y – x – 8 – 3 end cell equals 0 row cell 2 y – x – 11 end cell equals 0 end table end style 

Jadi, persamaan garis singgungnya adalah begin mathsize 14px style 2 y minus x minus 11 equals 0 end style.

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved