Answer
$\frac{f(a+h)-f(a)}{h}=6a+3h$
Work Step by Step
We are given:
$f(x)=3x^{2}+2$
We evaluate:
$f(a)=3a^{2}+2$
$f(a+h)=3(a+h)^{2}+2=3a^{2}+6ah+3h^{2}+2$
$\frac{f(a+h)-f(a)}{h}=\frac{(3a^{2}+6ah+3h^{2}+2)-(3a^{2}+2)}{h}=\frac{6ah+3h^{2}}{h}=\frac{h(6a+3h)}{h}=6a+3h$
