Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h≠0, for the following function. be sure to simplify. f(x)= - 2x² + 2x + 2 $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

$f(x + h)=-2(x + h)^2+2(x + h)+2=-2(x^{2}+2xh+h^{2})+2x + 2h+2=-2x^{2}-4xh-2h^{2}+2x + 2h+2$

Step2: Calculate f(x + h) - f(x)

$f(x + h)-f(x)=(-2x^{2}-4xh-2h^{2}+2x + 2h+2)-(-2x^{2}+2x + 2)=-4xh-2h^{2}+2h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-4xh-2h^{2}+2h}{h}=-4x-2h + 2$

Answer:

$-4x-2h + 2$