Question

Find and simplify the difference quotient for the given function

Answer 1

$\dfrac{f(x+h)+f(x)}{h}$

Replace f(x) and f(x+h) by using the equation given for the problem.

$=\dfrac{(2(x+h)^2-(x+h)-1)-(2x^2-x-1)}{h}$

Open all parenthesis

$= \dfrac{2x^2+4xh+2h^2-x-h-1-2x^2+x+1}{h}$

Factor the h

$= \dfrac{h(4x+2h-1)+2x^2-2x^2+1-1+x-x}{h}$

Other terms not in the parenthesis cancel each other out

$\dfrac{h(4x+2h-1)}{h}$

Now, simplify

$=4x+2h-1$