Answer
$6x+3h-2$
Work Step by Step
The difference quotient is the first step to find the derivative of a function.
The quotient itself can be expressed by the fraction $\dfrac{f(x+h)-f(x)}{h}$, where $h\ne0$.
If we take the given function and substitute it into the fraction we get:
$\dfrac{3(x+h)^2-2(x+h)+6-(3x^2-2x+6)}{h}
\\=\dfrac{3(x^2+2xh+h^2)-2x-2h+6-3x^2+2x-6}{h}
\\=\dfrac{6xh+3h^2-2h}{h}\\
=6x+3h-2$.
Thus, the difference quotient is $6x+3h-2$.
