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Question Number 69979 by Maclaurin Stickker last updated on 29/Sep/19

$$Usingthedefinitioncalculatethe$$$$derivativeatpointx=2$$$$f\left(x\right)=2x^3$$$$$$

Commented by kaivan.ahmadi last updated on 29/Sep/19

$${lim}_{x\to 2}\frac{f\left(x\right)-f\left(2\right)}{x-2}={lim}_{x\to 2}\frac{2x^3-16}{x-2}=$$$${lim}_{x\to 2}\frac{2(x-2)(x^2+2x+4)}{x-2}={lim}_{x\to 2}2(x^2+2x+4)=$$$$2(4+4+4)=24$$

Commented by Rio Michael last updated on 29/Sep/19

$$f{}^{{}^{\prime }}\left(x\right)=6x^2\Rightarrow f{}^{{}^{\prime }}\left(2\right)=24$$

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