## Precalculus (10th Edition)

$6x+3h$
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: $\dfrac{f(x+h)-f(x)}{h}\\ =\dfrac{[3(x+h)^2+2]-(3x^2+2)}{h}\\ =\dfrac{[3(x^2+2xh+h^2)+2]-(3x^2+2)}{h}\\ =\dfrac{3x^2+6xh+3h^2+2-3x^2-2}{h}\\ =\dfrac{6xh+3h^2}{h}\\ =\dfrac{h(6x+3h)}{h}\\ =6x+3h$