Roboguru

Diketahui fungsi . Persamaan garis singgung grafik fungsi  di titik  adalah...

Pertanyaan

Diketahui fungsi f open parentheses x close parentheses equals fraction numerator sin space open parentheses x minus begin display style straight pi over 2 end style close parentheses over denominator 1 plus cos space open parentheses x minus begin display style straight pi over 2 end style close parentheses end fraction. Persamaan garis singgung grafik fungsi f di titik x equals 0 adalah...

  1. y equals x minus 2 

  2. y equals x minus 1 

  3. y equals x 

  4. y equals x plus 1 

  5. y equals x plus 2 

Pembahasan Soal:

Turunan Pertama pada Fungsi Trigonometri

Fungsi f open parentheses x close parentheses equals fraction numerator sin space open parentheses x minus begin display style straight pi over 2 end style close parentheses over denominator 1 plus cos space open parentheses x minus begin display style straight pi over 2 end style close parentheses end fraction, gunakan sifta turunan untuk menentukan turunan pertama.

Turunan f open parentheses x close parentheses equals u over v adalah f apostrophe open parentheses x close parentheses equals fraction numerator v u apostrophe minus u v apostrophe over denominator v squared end fraction.

Misal u equals sin space open parentheses x minus straight pi over 2 close parentheses, maka u apostrophe equals cos space open parentheses x minus straight pi over 2 close parentheses.

Dan v equals 1 plus cos space open parentheses x minus straight pi over 2 close parentheses, maka v apostrophe equals negative sin space open parentheses x minus straight pi over 2 close parentheses.

Dimisalkan x minus straight pi over 2 equals theta, sehingga diperoleh turunan pertama

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator v u apostrophe minus u v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus cos space theta close parentheses open parentheses cos space theta close parentheses minus open parentheses sin space theta close parentheses open parentheses negative sin space theta close parentheses over denominator open parentheses 1 plus cos space theta close parentheses squared end fraction end cell row blank equals cell fraction numerator cos space theta plus cos squared space theta plus sin squared space theta over denominator open parentheses 1 plus cos space theta close parentheses open parentheses 1 plus cos space theta close parentheses end fraction end cell row blank equals cell fraction numerator cos space theta plus 1 over denominator open parentheses 1 plus cos space theta close parentheses open parentheses 1 plus cos space theta close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus cos space theta over denominator open parentheses 1 plus cos space theta close parentheses open parentheses 1 plus cos space theta close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus cos space theta end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus cos space open parentheses x minus begin display style straight pi over 2 end style close parentheses end fraction end cell end table  

Menentukan Koordinat Titik Singgung

 x equals 0, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 0 close parentheses end cell equals cell fraction numerator sin space open parentheses x minus begin display style straight pi over 2 end style close parentheses over denominator 1 plus cos space open parentheses x minus begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator sin space open parentheses 0 minus begin display style straight pi over 2 end style close parentheses over denominator 1 plus cos space open parentheses 0 minus begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator sin space open parentheses negative begin display style straight pi over 2 end style close parentheses over denominator 1 plus cos space open parentheses negative begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 plus 0 end fraction end cell row blank equals cell negative 1 end cell end table 

Koordinat titik singgungnya adalah open parentheses 0 comma negative 1 close parentheses.

Menentukan gradien 

table attributes columnalign right center left columnspacing 0px end attributes row m equals cell f apostrophe open parentheses 0 close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 plus cos space open parentheses x minus begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus cos space open parentheses 0 minus begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus cos space open parentheses negative begin display style straight pi over 2 end style close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 plus 0 end fraction end cell row blank equals 1 end table 

Persamaan Garis Singgung

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 open parentheses negative 1 close parentheses end cell equals cell 1 open parentheses x minus 0 close parentheses end cell row cell y plus 1 end cell equals cell x minus 0 end cell row y equals cell x minus 1 end cell end table 

Jadi, persamaan garis singgung grafik fungsi f di titik x equals 0 adalah y equals x minus 1.

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 13 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 kurva  di titik .

Pembahasan Soal:

Persamaan garis singgung di titik begin mathsize 14px style left parenthesis a comma b right parenthesis end style pada kurva begin mathsize 14px style y equals f left parenthesis x right parenthesis end style adalah begin mathsize 14px style left parenthesis y minus b right parenthesis equals m left parenthesis x minus a right parenthesis end style dengan begin mathsize 14px style m equals f apostrophe left parenthesis x right parenthesis end style

Diketahui

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell square root of 3 cos x minus sin x end cell row blank equals cell f left parenthesis x right parenthesis end cell end table end style 

Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row m equals cell f apostrophe left parenthesis x right parenthesis end cell row blank equals cell square root of 3 open parentheses negative sin x close parentheses minus cos x end cell row blank equals cell negative square root of 3 sin x minus cos x end cell end table end style

Untuk begin mathsize 14px style x equals 1 third straight pi end style diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row m equals cell negative square root of 3 sin open parentheses 1 third straight pi close parentheses minus cos open parentheses 1 third straight pi close parentheses end cell row blank equals cell negative square root of 3 open parentheses 1 half square root of 3 close parentheses minus 1 half end cell row blank equals cell negative 3 over 2 minus 1 half end cell row blank equals cell negative 2 end cell end table end style

Sehingga didapat 

undefined 

Jadi, persamaan garis singgungnya adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold y end table table attributes columnalign right center left columnspacing 0px end attributes row blank bold equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold italic x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bold left parenthesis bold 2 over bold 3 bold pi bold plus bold 1 bold right parenthesis end cell end table end style 

0

Roboguru

Tentukan persamaan garis singgung kurva  pada titik dimana

Pembahasan Soal:

Pertama kita tentukan titik singgung, dengan mensubtitusi nilai begin mathsize 14px style x equals straight pi over 4 end style ke persmaan kurva:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell cotan squared space x plus 2 space cotan space x end cell row cell f open parentheses straight pi over 4 close parentheses end cell equals cell c o tan squared open parentheses straight pi over 4 close parentheses plus 2 c o tan open parentheses straight pi over 4 close parentheses end cell row y equals cell open parentheses 1 close parentheses squared plus 2 open parentheses 1 close parentheses end cell row y equals 3 end table

Sehingga titik singgungnya adalah open curly brackets straight pi over 4 comma 3 close curly brackets

Kemudian, ingat bahwa: m equals f apostrophe open parentheses x close parentheses

Sehingga kita menentukan turunan dari y equals cotan squared space x plus 2 space cotan space x

y equals cotan squared space x plus 2 space cotan space x f apostrophe left parenthesis x right parenthesis equals 2 c o tan space x open parentheses negative cos e c squared x close parentheses minus 2 space cos e c squared space x f apostrophe left parenthesis x right parenthesis equals negative 2 c o tan x times cos e c squared x minus 2 space cos e c squared x

Sehingga gradien garis pada saat begin mathsize 14px style x equals straight pi over 4 end style adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative 2 c o tan x times cos e c squared x minus 2 space cos e c squared x end cell row cell f apostrophe open parentheses straight pi over 4 close parentheses end cell equals cell negative 2 c o tan open parentheses straight pi over 4 close parentheses times cos e c squared open parentheses straight pi over 4 close parentheses minus 2 space cos e c squared open parentheses straight pi over 4 close parentheses end cell row m equals cell negative 2 open parentheses 1 close parentheses times open parentheses square root of 2 close parentheses squared minus 2 open parentheses square root of 2 close parentheses squared end cell row m equals cell negative 2 times 2 minus 2 times 2 end cell row m equals cell negative 8 end cell end table

Sehingga, gradien garis tersbut adalah negative 8 

Selanjutnya dengan menggunkan persmaan garis lurus:

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 3 end cell equals cell negative 8 open parentheses x minus straight pi over 4 close parentheses end cell row y equals cell negative b x plus straight pi over 4 plus 3 end cell end table

Jadi, persamaan garis singgung kurva tersebut adalah adalah y equals negative b x plus straight pi over 4 plus 3

 

0

Roboguru

Tentukan persamaan garis singgung pada kurva  di titik !

Pembahasan Soal:

Gradien garis singgung kurva dapat diketahui dengan m equals f apostrophe left parenthesis x right parenthesis. Sedangkan apabila garis singgung memiliki titik open parentheses a comma b close parentheses maka persamaan garis singgungnya adalah :

y minus b equals m left parenthesis x minus a right parenthesis

Diketahui f left parenthesis x right parenthesis equals negative 2 space cos space 3 x, maka m equals f apostrophe left parenthesis x right parenthesis :

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell negative 2 space cos space 3 x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 6 space sin space 3 x end cell end table

Titik open parentheses straight pi over 4 comma space square root of 2 close parentheses, maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 6 space sin space 3 x end cell row cell f apostrophe open parentheses straight pi over 4 close parentheses end cell equals cell 6 space sin space 3 open parentheses straight pi over 4 close parentheses end cell row blank equals cell 6 space sin space 135 end cell row blank equals cell 6 cross times 1 half square root of 2 end cell row blank equals cell 3 square root of 2 end cell end table

Persamaan garis singgungnya :

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus b end cell equals cell m left parenthesis x minus a right parenthesis end cell row cell y minus square root of 2 end cell equals cell 3 square root of 2 open parentheses straight x minus straight pi over 4 close parentheses end cell row y equals cell 3 square root of 2 open parentheses straight x minus straight pi over 4 close parentheses plus square root of 2 end cell end table

Maka, persamaan garis singgungnya adalah table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 square root of 2 open parentheses straight x minus straight pi over 4 close parentheses plus square root of 2 end cell end table.

0

Roboguru

Diketahui kurva  melalui titik berabsis . Persamaan garis singgung kurva pada titik tersebut adalah...

Pembahasan Soal:

Tentukan titik singgung, absis straight pi over 2. Ingatlah!

cos open parentheses pi over 2 close parentheses equals 0

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell cos squared x minus 2 cos x minus 1 end cell row y equals cell cos squared x minus 2 cos x minus 1 end cell row blank equals cell cos squared open parentheses straight pi over 2 close parentheses minus 2 cos open parentheses straight pi over 2 close parentheses minus 1 end cell row blank equals cell 0 squared minus 2 times thin space 0 minus 1 end cell row blank equals cell negative 1 end cell end table

Di dapatkan titik open parentheses x subscript 1 comma y subscript 1 close parentheses equals open parentheses straight pi over 2 comma negative 1 close parentheses

Tentukan turunan pertama dari f left parenthesis x right parenthesis equals cos squared x minus 2 cos x minus 1. Ingatlah!

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell u squared end cell row u equals cell cos left parenthesis negative 2 cos left parenthesis x right parenthesis minus 1 right parenthesis end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator d over denominator d x end fraction open parentheses cos squared open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell row blank equals cell fraction numerator d over denominator d u end fraction open parentheses u squared close parentheses fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell row blank equals cell 2 u to the power of 2 minus 1 end exponent fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell row blank equals cell 2 u fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell row blank equals cell 2 cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell end table

Kemudian cari turunan fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell cos space u end cell row u equals cell negative 2 cos left parenthesis x right parenthesis minus 1 end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator d over denominator d x end fraction open parentheses cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses end cell row blank equals cell negative sin open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses end cell row blank equals cell negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times fraction numerator d over denominator d x end fraction open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses end cell row blank equals cell negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times negative fraction numerator d over denominator d x end fraction open parentheses 2 cos open parentheses x close parentheses close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses end cell row blank equals cell negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times negative 2 fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses close parentheses end cell row blank equals cell negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times negative 2 open parentheses negative sin open parentheses x close parentheses close parentheses end cell row blank equals cell negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times 2 sin open parentheses x close parentheses end cell end table

Di dapatkan,

fraction numerator d over denominator d x end fraction open parentheses cos squared open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses close parentheses equals 2 cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses open parentheses negative sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses times thin space 2 sin open parentheses x close parentheses close parentheses equals negative 4 cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses sin open parentheses x close parentheses

Tentukan gradien garis singgung melalui titik berabsis straight pi over 2

Ingatlah!

table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses pi over 2 close parentheses end cell equals 1 row cell cos open parentheses pi over 2 close parentheses end cell equals 0 row cell cos open parentheses x close parentheses sin open parentheses x close parentheses end cell equals cell fraction numerator sin open parentheses 2 x close parentheses over denominator 2 end fraction end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row m equals cell fraction numerator d y over denominator d x end fraction end cell row m equals cell negative 4 cos open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses sin open parentheses negative 2 cos open parentheses x close parentheses minus 1 close parentheses sin open parentheses x close parentheses end cell row blank equals cell negative 4 cos open parentheses negative 2 cos open parentheses straight pi over 2 close parentheses minus 1 close parentheses sin open parentheses negative 2 cos open parentheses straight pi over 2 close parentheses minus 1 close parentheses sin open parentheses straight pi over 2 close parentheses end cell row blank equals cell negative 4 cos open parentheses 2 cos open parentheses pi over 2 close parentheses plus 1 close parentheses sin open parentheses negative 2 cos open parentheses pi over 2 close parentheses minus 1 close parentheses sin open parentheses pi over 2 close parentheses end cell row blank equals cell negative 4 cos open parentheses 2 cos open parentheses pi over 2 close parentheses plus 1 close parentheses open parentheses negative sin open parentheses 2 cos open parentheses pi over 2 close parentheses plus 1 close parentheses close parentheses sin open parentheses pi over 2 close parentheses end cell row blank equals cell 4 sin open parentheses pi over 2 close parentheses cos open parentheses 2 cos open parentheses pi over 2 close parentheses plus 1 close parentheses sin open parentheses 2 cos open parentheses pi over 2 close parentheses plus 1 close parentheses end cell row blank equals cell 4 times thin space 1 times cos open parentheses 2 times thin space 0 plus 1 close parentheses sin open parentheses 2 times thin space 0 plus 1 close parentheses end cell row blank equals cell 4 cos open parentheses 1 close parentheses sin open parentheses 1 close parentheses end cell row blank equals cell 4 times fraction numerator sin open parentheses 2 times thin space 1 close parentheses over denominator 2 end fraction end cell row blank equals cell 4 times fraction numerator sin open parentheses 2 close parentheses over denominator 2 end fraction end cell row blank equals cell 2 sin open parentheses 2 close parentheses end cell row blank equals cell 1 comma 8 end cell row blank almost equal to 2 end table

Di dapatkan gradien garis singgung m equals 2 dan titik open parentheses x subscript 1 comma y subscript 1 close parentheses equals open parentheses straight pi over 2 comma negative 1 close parentheses. Persamaan garis singgung, 

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 left parenthesis negative 1 right parenthesis end cell equals cell 2 open parentheses x minus straight pi over 2 close parentheses end cell row cell y plus 1 end cell equals cell 2 open parentheses x minus straight pi over 2 close parentheses end cell row y equals cell 2 open parentheses x minus straight pi over 2 close parentheses minus 1 end cell row y equals cell 2 x minus fraction numerator 2 straight pi over denominator 2 end fraction minus 1 end cell row y equals cell 2 x minus straight pi minus 1 end cell end table

Jadi, persamaan garis singgung kurva pada titik tersebut adalah y equals 2 x minus straight pi minus 1.


Oleh karena itu, jawaban yang benar adalah C.

1

Roboguru

Diketahui  untuk interval . Tentukan: a. Gradien garis singgung grafik  di titik . b. Persamaan garis singgung grafik  di titik .

Pembahasan Soal:

a. Gradien garis singgung grafik f open parentheses x close parentheses di titik x equals straight pi over 2

Turunan Pertama pada Fungsi Trigonometri

Fungsi f open parentheses x close parentheses equals sin space open parentheses 2 x minus straight pi close parentheses space cos space open parentheses x minus straight pi over 2 close parentheses, dimisalkan:

u equals sin space open parentheses 2 x minus straight pi close parentheses maka u apostrophe equals 2 space cos space open parentheses 2 x minus straight pi close parentheses.

v equals cos space open parentheses x minus straight pi over 2 close parentheses maka v apostrophe equals negative sin space open parentheses x minus straight pi over 2 close parentheses.

Sehingga dengan sifat turunan f open parentheses x close parentheses equals u times v diperoleh turunan pertama

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell v u apostrophe plus u v apostrophe end cell row blank equals cell open parentheses cos space open parentheses x minus straight pi over 2 close parentheses close parentheses open parentheses 2 space cos space open parentheses 2 x minus straight pi close parentheses close parentheses plus end cell row blank blank cell open parentheses sin space open parentheses 2 x minus straight pi close parentheses close parentheses open parentheses negative sin space open parentheses x minus straight pi over 2 close parentheses close parentheses end cell row blank equals cell 2 space cos space open parentheses 2 x minus straight pi close parentheses space cos space open parentheses x minus straight pi over 2 close parentheses minus end cell row blank blank cell sin space open parentheses 2 x minus straight pi close parentheses space sin space open parentheses x minus straight pi over 2 close parentheses end cell end table  

Gradien Garis Singgung Grafik

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell 2 space cos space open parentheses 2 x minus straight pi close parentheses space cos space open parentheses x minus straight pi over 2 close parentheses end cell end tabletable attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative sin space open parentheses 2 x minus straight pi close parentheses space sin space open parentheses x minus straight pi over 2 close parentheses end cell end table sehingga nilai gradien sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses straight pi over 2 close parentheses end cell equals cell 2 space cos space open parentheses 2 open parentheses straight pi over 2 close parentheses minus straight pi close parentheses space cos space open parentheses open parentheses straight pi over 2 close parentheses minus straight pi over 2 close parentheses minus end cell row blank blank cell sin space open parentheses 2 open parentheses straight pi over 2 close parentheses minus straight pi close parentheses space sin space open parentheses open parentheses straight pi over 2 close parentheses minus straight pi over 2 close parentheses end cell row blank equals cell 2 space cos space 0 space cos space 0 minus sin space 0 space sin space 0 end cell row blank equals cell 2 open parentheses 1 close parentheses open parentheses 1 close parentheses minus 0 open parentheses 0 close parentheses end cell row blank equals 2 end table   

Dengan demikian, diperoleh gradien m equals 2.

b. Persamaan garis singgung grafik f open parentheses x close parentheses di titik x equals straight pi over 2

Untuk x equals straight pi over 2, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses straight pi over 2 close parentheses end cell equals cell sin space open parentheses 2 open parentheses straight pi over 2 close parentheses minus straight pi close parentheses space cos space open parentheses open parentheses straight pi over 2 close parentheses minus straight pi over 2 close parentheses end cell row blank equals cell sin space 0 space cos space 0 end cell row blank equals cell 0 open parentheses 1 close parentheses end cell row blank equals 0 end table 

Persamaan garis singgung fungsi di titik open parentheses straight pi over 2 comma 0 close parentheses sebagai berikut:

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 0 end cell equals cell 2 open parentheses x minus straight pi over 2 close parentheses end cell row y equals cell 2 x minus straight pi end cell end table 

Dengan demikian, persamaan garis singgung fungsi di titik straight pi over 2 adalah y equals 2 x minus straight pi.

0

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