Answer
$-4x-2h+1.$
Work Step by Step
$\frac{f(x+h)-f(x)}{h}=\frac{(-2(x+h)^2+(x+h)+1)-(-2x^2+x+1)}{h}=\frac{(-2x^2-4xh-2h^2+x+h+1)+2x^2-x-1)}{h}=\frac{-4xh-2h^2+h}{h}=-4x-2h+1.$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.