Question

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

Answer 1

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