Pertanyaan

Gradien garis singgung kurva y = 3 x 2 di titik (2,12) adalah ….

Gradien garis singgung kurva $y = 3 x^{2}$ di titik (2,12) adalah ….

R. RGFLSATU

Master Teacher

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Pembahasan

Diketahui Maka Sehingga diperoleh turunan kurva terebut adalah Jadi, gradien garis singgung kurva di titik (2,12) adalah m = 6(2) = 12.

Diketahui

Maka

Sehingga diperoleh turunan kurva terebut adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight h rightwards arrow 0 of fraction numerator straight f left parenthesis straight x plus straight h right parenthesis minus straight f left parenthesis straight x right parenthesis over denominator straight h end fraction end cell equals cell limit as straight h rightwards arrow 0 of fraction numerator 3 left parenthesis straight x plus straight h right parenthesis squared minus 3 straight x squared over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of fraction numerator 3 left parenthesis straight x squared plus 2 xh plus straight h squared right parenthesis minus 3 straight x squared over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of fraction numerator 3 straight x squared plus 6 xh plus 3 straight h squared minus 3 straight x squared over denominator straight h end fraction end cell row blank equals cell limit as straight h rightwards arrow 0 of left parenthesis fraction numerator 6 xh plus 3 straight h squared over denominator straight h end fraction right parenthesis end cell row blank equals cell limit as straight h rightwards arrow 0 of left parenthesis fraction numerator straight h open parentheses 6 straight x plus 3 straight h close parentheses over denominator straight h end fraction right parenthesis end cell row blank equals cell limit as straight h rightwards arrow 0 of left parenthesis 6 straight x plus 3 straight h right parenthesis end cell row blank equals cell 6 straight x end cell end table end style$

Jadi, gradien garis singgung kurva di titik (2,12) adalah m = 6(2) = 12.