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Pertanyaan

Persamaan garis singgung kurva  begin mathsize 14px style f open parentheses x close parentheses equals square root of x cubed end root minus 2 end style di absis 1 memotong sumbu-y di titik ….

  1. begin mathsize 14px style open parentheses 0 comma 5 over 2 close parentheses end style

  2. begin mathsize 14px style open parentheses 0 comma negative 2 over 5 close parentheses end style 

  3. undefined 

  4. begin mathsize 14px style open parentheses 1 comma 5 over 2 close parentheses end style

  5. begin mathsize 14px style open parentheses 1 comma 2 over 5 close parentheses end style

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Pertama, turunkan begin mathsize 14px style f open parentheses x close parentheses equals square root of x cubed end root minus 2 end style.

begin mathsize 14px style f open parentheses x close parentheses equals square root of x cubed end root minus 2 f open parentheses x close parentheses equals x to the power of 3 over 2 end exponent minus 2 f to the power of apostrophe open parentheses x close parentheses equals 3 over 2 times x to the power of 3 over 2 minus 1 end exponent minus 0 f to the power of apostrophe open parentheses x close parentheses equals 3 over 2 x to the power of 1 half end exponent end style

 

Kedua, hitung gradien garis singgung kurva di titik x = 1.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of apostrophe open parentheses 1 close parentheses end cell equals cell 3 over 2 times open parentheses 1 close parentheses to the power of 1 half end exponent end cell row cell m subscript g end cell equals cell 3 over 2 end cell 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 end style = 1.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses end cell equals cell square root of 1 cubed end root minus 2 end cell row y equals cell negative 1 end cell end table end style

 

Keempat, buat persamaan garis singgung di titik (begin mathsize 14px style x subscript 1 end stylebegin mathsize 14px style y subscript 1 end style) = (1, -1).

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px y size 14px minus size 14px y subscript size 14px 1 end cell size 14px equals cell size 14px m subscript size 14px g begin mathsize 14px style left parenthesis x minus x subscript 1 right parenthesis end style end cell row cell size 14px y size 14px plus size 14px 1 end cell size 14px equals cell size 14px 3 over size 14px 2 begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style end cell row cell size 14px 2 begin mathsize 14px style left parenthesis y plus 1 right parenthesis end style end cell size 14px equals cell size 14px 3 begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style end cell row cell size 14px 2 size 14px y size 14px plus size 14px 2 end cell size 14px equals cell size 14px 3 size 14px x size 14px minus size 14px 3 end cell row cell size 14px 2 size 14px y end cell size 14px equals cell size 14px 3 size 14px x size 14px minus size 14px 5 end cell row cell size 14px 2 size 14px y size 14px minus size 14px 3 size 14px x size 14px plus size 14px 5 end cell size 14px equals size 14px 0 end table 

 

Kelima, hitung perpotongan garis singgung dengan sumbu-y yaitu saat x = 0.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 y minus 3 x plus 5 end cell equals 0 row cell 2 y minus 3 left parenthesis 0 right parenthesis plus 5 end cell equals 0 row cell 2 y plus 5 end cell equals 0 row cell 2 y end cell equals cell negative 5 end cell row y equals cell negative 5 over 2 end cell end table end style 

Jadi, perpotongan garis singgung tersebut dengan sumbu-y di titik begin mathsize 14px style open parentheses 0 comma negative 5 over 2 close parentheses end style.

Oleh karena itu, jawaban yang tepat adalah C.

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