Answer
$-4x-2h+1$
Work Step by Step
We find the difference quotient as follows:
$\displaystyle \frac{f(x+h)-f(x)}{h} =\frac{-2(x+h)^2+(x+h)+1-(-2x^2+x+1)}{h} \\=\dfrac{-2(x^2+h^2+2h)+(x+h)+1-(-2x^2+x+1)}{h} \\=\dfrac{-2x^2-4xh-2h^2+x+h+1+2x^2-x-1}{h} \\=\dfrac{-4xh-2h^2+h}{h} \\=-4x-2h+1$
