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\$\$

So,

\$\$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?

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answered Oct 10 "16 at 15:40

danwalkerdevdanwalkerdev
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