Pertanyaan

Dengan menggunakan konsep limit fungsi, tentukan gradien garis singgung fungsi berikut. f ( x ) = 2 ( 1 − x ) 2

Dengan menggunakan konsep limit fungsi, tentukan gradien garis singgung fungsi berikut.

$f (x) = 2 (1 - x)^{2}$

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Jawaban terverifikasi

Pembahasan

Gradien garis singgung fungsi dengan menggunakan konsep limit fungsi adalah Maka gradien garis singgungnya adalah .

Gradien garis singgung fungsi dengan menggunakan konsep limit fungsi adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript A end cell equals cell limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open square brackets 2 open parentheses 1 minus open parentheses x plus h close parentheses close parentheses squared close square brackets minus open square brackets 2 open parentheses 1 minus x close parentheses squared close square brackets over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open square brackets 2 open parentheses 1 minus open parentheses x plus h close parentheses close parentheses squared close square brackets minus 2 open parentheses 1 minus x close parentheses squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open square brackets 2 left parenthesis 1 minus 2 open parentheses x plus h close parentheses plus open parentheses x plus h close parentheses squared close square brackets minus 2 open parentheses 1 minus 2 x plus x squared close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 minus 4 open parentheses x plus h close parentheses plus 2 open parentheses x squared plus 2 x h plus h squared close parentheses minus 2 plus 2 x minus x squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 minus 4 x minus 4 h plus 2 x squared plus 4 x h plus 2 h squared minus 2 plus 2 x minus x squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative 4 h plus 4 x h plus 2 h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of minus 4 plus 4 x plus 2 h end cell row blank equals cell negative 4 minus 4 x end cell row blank equals cell negative 4 left parenthesis 1 minus x right parenthesis end cell end table end style$

Maka gradien garis singgungnya adalah .