Answer
$6x+3h$
Work Step by Step
RECALL:
$\\\\$The difference quotient of a function $f$ is given by the formula $\dfrac{f(x+h)-f(x)}{h}$ where $h \ne0$.
Use the difference quotient formula above to obtain:
$\dfrac{f(x+h)-f(x)}{h}\\
=\dfrac{[3(x+h)^2+2]-(3x^2+2)}{h}\\
=\dfrac{[3(x^2+2xh+h^2)+2]-(3x^2+2)}{h}\\
=\dfrac{3x^2+6xh+3h^2+2-3x^2-2}{h}\\
=\dfrac{6xh+3h^2}{h}\\
=\dfrac{h(6x+3h)}{h}\\
=6x+3h$
