Answer
$\frac{f(a+h)-f(a)}{h}=3a^{2}+3ah+h^{2}$
Work Step by Step
We are given:
$f(x)=x^3$
We evaluate:
$f(a)=a^{3}$
$f(a+h)=(a+h)^{3}=a^{3}+3a^{2}h+3ah^{2}+h^{3}$
$\frac{f(a+h)-f(a)}{h}=\frac{(a^{3}+3a^{2}h+3ah^{2}+h^{3})-(a^{3})}{h}=\frac{3a^{2}h+3ah^{2}+h^{3}}{h}=
\frac{h(3a^{2}+3ah+h^{2})}{h}=3a^{2}+3ah+h^{2}$
