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Pertanyaan

Persamaan garis singgung dari fungsi f left parenthesis x right parenthesis equals cos to the power of 4 x pada x equals straight pi over 4 adalah...

  1. y plus x minus 1 minus straight pi equals 0

  2. 4 y plus x minus 1 minus straight pi equals 0

  3. 4 y plus 4 x plus 1 plus straight pi equals 0

  4. 4 y plus 4 x minus 1 minus straight pi equals 0

  5. 4 y plus x plus 1 minus straight pi equals 0

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Tentukan titik singgung, karena x equals straight pi over 4 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell cos to the power of 4 x end cell row y equals cell cos to the power of 4 x end cell row blank equals cell cos to the power of 4 open parentheses straight pi over 4 close parentheses end cell row blank equals cell cos to the power of 4 open parentheses 180 over 4 close parentheses end cell row blank equals cell cos to the power of 4 open parentheses 45 close parentheses end cell row blank equals cell open parentheses 1 half square root of 2 close parentheses to the power of 4 end cell row blank equals cell 1 over 16 times 2 squared end cell row blank equals cell 4 over 16 end cell row blank equals cell 1 fourth end cell end table

Di dapatkan titik singgungnya open parentheses x subscript 1 comma y subscript 1 close parentheses equals open parentheses straight pi over 4 comma 1 fourth close parentheses. Kemudian tentukan turunan pertama dari f left parenthesis x right parenthesis equals cos to the power of 4 x

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses cos to the power of 4 open parentheses x close parentheses close parentheses end cell equals cell 4 open parentheses cos open parentheses x close parentheses close parentheses cubed 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 4 open parentheses cos open parentheses x close parentheses close parentheses cubed open parentheses negative sin open parentheses x close parentheses close parentheses end cell row blank equals cell negative 4 cos cubed open parentheses x close parentheses sin open parentheses x close parentheses end cell end table

Tentukan gradiennya,

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 blank equals cell negative 4 cos cubed open parentheses x close parentheses sin open parentheses x close parentheses end cell row blank equals cell negative 4 cos cubed open parentheses straight pi over 4 close parentheses sin open parentheses straight pi over 4 close parentheses end cell row blank equals cell negative 4 cos cubed open parentheses 45 degree close parentheses sin open parentheses 45 degree close parentheses end cell row blank equals cell negative 4 open parentheses 1 half square root of 2 close parentheses cubed open parentheses 1 half square root of 2 close parentheses end cell row blank equals cell negative 4 open parentheses 3 over 2 square root of 2 close parentheses open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses end cell row blank equals cell negative 4 open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses to the power of 4 end cell row blank equals cell negative 4 times 1 over 2 squared end cell row blank equals cell fraction numerator negative 4 over denominator 4 end fraction end cell row blank equals cell negative 1 end cell 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 left parenthesis x minus x subscript 1 right parenthesis end cell row cell y minus 1 fourth end cell equals cell negative 1 open parentheses x minus straight pi over 4 close parentheses end cell row y equals cell negative straight x plus straight pi over 4 plus 1 fourth end cell row cell 4 straight y end cell equals cell negative 4 straight x plus straight pi plus 1 end cell row cell 4 straight y plus 4 straight x minus straight pi minus 1 end cell equals 0 end table

Jadi, persamaan garis singgungnya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

 

Oleh karena itu, jawaban yang benar adalah D.

99

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