Use the alternate develop of the derivative to uncover the derivative at $x=c$ if $f(x)=x^3+4x$ and $c=2$.

You are watching: Use the alternative form of the derivative to find the derivative at x = c

I keep gaining stuck with the answer being $0$, no issue how I attempt to fix it. If someone could please use step-by-step instructions to aid me view what I"m doing wrong, that would be great. Thank you!



From resources digital I deserve to just translate the "alternative" create as this:

$$f^prime(x) = lim_x o c fracf(x)-f(c)x-c$$


$$eginalignf^prime(2) &= lim_x o 2 fracx^3 + 4x - (2^3 + 4 cdot 2))x - 2\&= lim_x o 2 fracx^3 + 4x - 16x - 2\&= lim_x o 2 frac(x-2)(x^2 + 2x + 8)x-2\&= lim_x o 2 , (x^2 + 2x + 8)\&= 16endalign$$

The important step is cancelling the $x-2$ in the denominator, notification we deserve to perform this because $x-2 eq 0$ as we are considering the limit. Can you watch which allude you were struggling at?

answered Oct 10 "16 at 15:40

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