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Persamaan garis singgung kurva y = x 3 − 3 x − 2 yang sejajar dengan garis − y + 5 x + 31 = 0 adalah....

Persamaan garis singgung kurva yang sejajar dengan garis adalah....
 

  1. x minus 5 y plus 3 equals 0

  2. x minus 5 y plus 6 equals 0

  3. 5 x minus y minus 6 equals 0

  4. 5 x minus y minus 12 equals 0

  5. 5 x minus y minus 18 equals 0

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N. Puspita

Master Teacher

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Karena sejajar maka gradiennya sama, Kemudian cari turunan dari Subtitusikan gradien ke persamaan, Subtitusikan nilai pada persamaan kurva : Untuk Untuk Persamaan garis singgung melalui dapat disusun dengan rumus: Untuk dan , maka: Untuk dan , maka: Persamaan garis singgungnya adalah dan . Jadi, tidak ada pilihan jawaban yang tepat.

Karena sejajar maka gradiennya sama, 

table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript 1 end cell equals cell m subscript 2 end cell row cell negative y plus 5 x plus 31 end cell equals 0 row y equals cell 5 x plus 31 end cell row y equals cell m x plus c end cell row m equals 5 end table

Kemudian cari turunan dari y equals x cubed minus 3 x minus 2

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x cubed minus 3 x minus 2 end cell row cell y apostrophe end cell equals cell 3 x to the power of 3 minus 1 end exponent minus 3 x to the power of 1 minus 1 end exponent end cell row cell y apostrophe end cell equals cell 3 x squared minus 3 x to the power of 0 end cell row cell y apostrophe end cell equals cell 3 x squared minus 3 left parenthesis 1 right parenthesis end cell row cell y apostrophe end cell equals cell 3 x squared minus 3 end cell end table

Subtitusikan gradien ke persamaan,

table attributes columnalign right center left columnspacing 0px end attributes row 5 equals cell 3 x squared minus 3 end cell row cell 3 x squared minus 3 minus 5 end cell equals 0 row cell 3 x squared minus 8 end cell equals 0 row cell 3 x squared end cell equals 8 row cell x squared end cell equals cell 8 over 3 end cell row x equals cell plus-or-minus square root of 8 over 3 end root end cell row x equals cell plus-or-minus 1 comma 6 end cell row blank blank blank end table

Subtitusikan nilai x pada persamaan kurva :

Untuk x equals 1 comma 6

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x cubed minus 3 x minus 2 end cell row y equals cell open parentheses 1 comma 6 close parentheses cubed minus 3 left parenthesis 1 comma 6 right parenthesis minus 2 end cell row y equals cell 4 comma 1 minus 4 comma 8 minus 2 end cell row y equals cell 4 comma 1 minus 6 comma 8 end cell row y equals cell negative 2 comma 7 end cell end table

Untuk x equals negative 1 comma 6

table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank cubed end cell 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 cell open parentheses negative 1 comma 6 close parentheses cubed minus 3 left parenthesis negative 1 comma 6 right parenthesis minus 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 minus 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 comma 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 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 comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 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 blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table

Persamaan garis singgung melalui left parenthesis x subscript 1 comma y subscript 1 right parenthesis dapat disusun dengan rumus:

y minus y subscript 1 equals m left parenthesis x minus x subscript 1 right parenthesis

Untuk x subscript 1 equals 1 comma 6 dan y subscript 1 equals negative 2 comma 7, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus left parenthesis negative 2 comma 7 right parenthesis end cell equals cell 5 left parenthesis x minus 1 comma 6 right parenthesis end cell row cell y plus 2 comma 7 end cell equals cell 5 x minus 8 end cell row y equals cell 5 x minus 8 minus 2 comma 7 end cell row 0 equals cell 5 x minus y minus 10 comma 7 end cell row cell 5 x minus y minus 10 comma 7 end cell equals 0 end table

Untuk x subscript 1 equals negative 1 comma 6 dan y subscript 1 equals negative 1 comma 3, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus left parenthesis negative 1 comma 3 right parenthesis end cell equals cell 5 left parenthesis x minus left parenthesis negative 1 comma 6 right parenthesis right parenthesis end cell row cell y plus 1 comma 3 end cell equals cell 5 left parenthesis x plus 1 comma 6 right parenthesis end cell row cell y plus 1 comma 3 end cell equals cell 5 x plus 8 end cell row y equals cell 5 x plus 8 minus 1 comma 3 end cell row 0 equals cell 5 x minus y plus 6 comma 7 end cell row cell 5 x minus y plus 6 comma 7 end cell equals 0 end table

Persamaan garis singgungnya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 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 y 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 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 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 dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 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 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 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 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. Jadi, tidak ada pilihan jawaban yang tepat.

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