Find the equation of the curve... (1 Viewer)

Utility · Jun 9, 2012

Given the point (2, -8) is a turning point of the curve y = f(x), f''(x) = 12x + 18.

qwerty44 · Jun 9, 2012

give me a sec to write solution

pokka · Jun 9, 2012

qwerty44 · Jun 9, 2012

$\begin{align*}&f''(x)=12x+18\\&f'(x)=6x^{2}+18x+c\\&f'(2)=6(2)^{2}+18(2)+c=0\\&c=-60\\&\therefore f'(x)=6x^{2}+18x-60\\\\&f(x)=2x^{3}+9x^{2}-60x+c\\&f(2)=2(2)^{3}+9(2)^{2}-60(2)+c=-8\\&c=60\\\\&\therefore f(x)=2x^{3}+9x^{2}-60x+60\end{align*}$

EDIT: Once again, im too slow.

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Find the equation of the curve... (1 Viewer)

Utility

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