find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h $
eq$ 0, for the following function. be sure to simplify. f(x)= - 2x$^{2}$ + 6x + 2 $\frac{f(x + h)-f(x)}{h}$ = (simplify your answer.)

Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h $
eq$ 0, for the following function. be sure to simplify. f(x)= - 2x$^{2}$ + 6x + 2 $\frac{f(x + h)-f(x)}{h}$ =  (simplify your answer.)

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute x+h into f(x):
$$
\begin{align*}
f(x + h)&=-2(x + h)^2+6(x + h)+2\
&=-2(x^{2}+2xh+h^{2})+6x + 6h+2\
&=-2x^{2}-4xh-2h^{2}+6x + 6h+2
\end{align*}
$$
## Step2: Calculate f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(-2x^{2}-4xh-2h^{2}+6x + 6h+2)-(-2x^{2}+6x + 2)\
&=-2x^{2}-4xh-2h^{2}+6x + 6h+2 + 2x^{2}-6x - 2\
&=-4xh-2h^{2}+6h
\end{align*}
$$
## Step3: Find the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{-4xh-2h^{2}+6h}{h}\
&=\frac{h(-4x-2h + 6)}{h}\
&=-4x-2h + 6
\end{align*}
$$
# Answer:
$-4x-2h + 6$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

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

Step3: Find the difference quotient

Answer: