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How do you use the definition of a derivative to find the derivative of $f(x)=x^3 + 2x^2 + 1$ , at c=-2?

1 Answer

Jan 24, 2016

4

Explanation:

f'(-2) = $lim h->0 (f(-2+h) -f(-2))/h$

= $lim h->0 ((-2+h)^3 +2(-2+h)^2 +1 - ( -8+8+1))/h$

= $lim h->0 (-8+12h-6h^2 +h^3 +2(4-4h+h^2 )+1 -1)/h$

= $lim h->0 (h^3 -4h^2 +4h)/h$

= 4

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