Answer
$12+6h+h^2$
Work Step by Step
$f(x) = x^3$
We can evaluate the difference quotient:
$\frac{f(2+h)- f(2)}{h}$
$= \frac{(2+h)^3- (2)^3}{h}$
$= \frac{(2+h)(2+h)(2+h)- 8}{h}$
$= \frac{(4+4h+h^2)(2+h)- 8}{h}$
$= \frac{8+4h+8h+4h^2+2h^2+h^3- 8}{h}$
$= \frac{12h+6h^2+h^3}{h}$
$= \frac{(h)(12+6h+h^2)}{h}$
$= 12+6h+h^2$
