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Persamaan garis singgung kurva undefined di absis begin mathsize 14px style 3 end style dan begin mathsize 14px style negative 3 end style akan saling berpotongan di titik ....

  1. begin mathsize 14px style left parenthesis negative 3 comma space 9 right parenthesis end style 

  2. begin mathsize 14px style left parenthesis negative 3 comma space 2 right parenthesis end style 

  3. begin mathsize 14px style left parenthesis 0 comma space 3 right parenthesis end style 

  4. begin mathsize 14px style left parenthesis 3 comma space 6 right parenthesis end style 

  5. begin mathsize 14px style left parenthesis 6 comma space 9 right parenthesis end style 

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.space space 

Pembahasan

Pertama, turunkan begin mathsize 14px style f left parenthesis x right parenthesis equals negative 1 third x squared end style

begin mathsize 14px style f to the power of apostrophe left parenthesis x right parenthesis equals 2 times negative 1 third x to the power of 2 minus 1 end exponent f to the power of apostrophe left parenthesis x right parenthesis equals negative 2 over 3 x end style

 

Kedua, hitung gradien garis singgung kurva di titik begin mathsize 14px style x equals 3 end style dan begin mathsize 14px style x equals negative 3 end style.

begin mathsize 14px style m blank subscript left parenthesis g subscript 1 right parenthesis end subscript equals f to the power of apostrophe left parenthesis 3 right parenthesis space space space space space space space space equals negative 2 over 3 open parentheses 3 close parentheses space space space space space space space space equals negative 2 end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript left parenthesis g subscript 2 right parenthesis end subscript end cell equals cell f to the power of apostrophe left parenthesis negative 3 right parenthesis end cell row blank equals cell negative 2 over 3 open parentheses negative 3 close parentheses end cell row blank equals 2 end table end style

 

Ketiga, hitung koordinat titik singgung begin mathsize 14px style y subscript 1 end style saat begin mathsize 14px style x subscript 1 equals 3 end style dan begin mathsize 14px style y subscript 2 end style saat begin mathsize 14px style x subscript 2 equals negative 3 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis 3 right parenthesis end cell 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 cell 1 third end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 3 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space space space y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript 1 end cell 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 3 end table end style

Diperoleh titik singgung pertama yaitu begin mathsize 14px style left parenthesis 3 comma space minus 3 right parenthesis end style.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 3 right parenthesis end cell equals cell negative 1 third left parenthesis negative 3 right parenthesis blank squared end cell row cell space space space space space space y blank subscript 2 end cell equals cell negative 3 end cell end table end style

Diperoleh titik singgung kedua yaitu begin mathsize 14px style left parenthesis negative 3 comma negative 3 right parenthesis end style.

 

Keempat, buat persamaan garis singgung di titik begin mathsize 14px style left parenthesis x comma space y right parenthesis equals left parenthesis 3 comma space minus 3 right parenthesis end style.

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 subscript g subscript 1 end subscript left parenthesis x minus x subscript 1 right parenthesis end cell row cell y minus left parenthesis negative 3 right parenthesis end cell equals cell negative 2 left parenthesis x minus 3 right parenthesis end cell row cell y plus 3 end cell equals cell negative 2 x plus 6 end cell row y equals cell negative 2 x plus 3 end cell end table end style

Diperoleh persamaan garis singgung pertama begin mathsize 14px style y equals negative 2 x plus 3 end style. Kemudian, buat juga persamaan garis singgung di titik begin mathsize 14px style left parenthesis x subscript 2 comma y subscript 2 right parenthesis equals left parenthesis negative 3 comma negative 3 right parenthesis end style.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 2 end cell equals cell m subscript g subscript 2 end subscript left parenthesis x minus x subscript 2 right parenthesis end cell row cell y plus 3 end cell equals cell 2 left parenthesis x plus 3 right parenthesis end cell row cell y plus 3 end cell equals cell 2 x plus 6 end cell row y equals cell 2 x plus 3 end cell end table end style

Diperoleh persamaan garis singgung kedua begin mathsize 14px style y equals 2 x plus 3 end style.

 

Kelima, hitung perpotongan kedua garis singgung tersebut.

undefined

Kemudian, titik y didapat dari mensubstitusi nilai x ke salah satu persamaan garis singgung kurva.

begin mathsize 14px style y equals 2 x plus 3 y equals 2 left parenthesis 0 right parenthesis plus 3 y equals 3 end style

Jadi, titik perpotongan kedua persamaan garis singgung tersebut pada koordinat undefined.

Jadi, jawaban yang tepat adalah C.space space 

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