Answer
$6x+3h-2$
Work Step by Step
We are given:
$f(x)=3x^{2}-2x+6$
We find the difference quotient:
$\displaystyle \frac{f(x+h)-f(x)}{h}$
$\displaystyle =\frac{[3(x+h)^{2}-2(x+h)+6]-[3x^{2}-2x+6]}{h}$
$\displaystyle =\frac{3(x^{2}+2xh+h^{2})-2x-2h+6-3x^{2}+2x-6}{h}$
$\displaystyle =\frac{3x^{2}+6xh+3h^{2}-2h-3x^{2}}{h}$
$\displaystyle =\frac{6xh+3h^{2}-2h}{h}$
$\displaystyle =\frac{h(6x+3h-2)}{h}$
$=6x+3h-2$
