find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h
eq0$, for the function below.

$f(x)=-x^{2}-2x + 5$

simplify your answer as much as possible.

$\frac{f(x + h)-f(x)}{h}=$

Question

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h
eq0$, for the function below.

$f(x)=-x^{2}-2x + 5$

simplify your answer as much as possible.

$\frac{f(x + h)-f(x)}{h}=$

Accepted Answer

# Explanation:
## Step1: Find $f(x + h)$
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=-(x + h)^2-2(x + h)+5\
&=-(x^{2}+2xh+h^{2})-2x-2h + 5\
&=-x^{2}-2xh - h^{2}-2x-2h + 5
\end{align*}
$$
## Step2: Calculate $f(x + h)-f(x)$
$$
\begin{align*}
f(x + h)-f(x)&=(-x^{2}-2xh - h^{2}-2x-2h + 5)-(-x^{2}-2x + 5)\
&=-x^{2}-2xh - h^{2}-2x-2h + 5 + x^{2}+2x - 5\
&=-2xh - h^{2}-2h
\end{align*}
$$
## Step3: Find the difference quotient $\frac{f(x + h)-f(x)}{h}$
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{-2xh - h^{2}-2h}{h}\
&=\frac{h(-2x - h - 2)}{h}\
&=-2x - h - 2
\end{align*}
$$
# Answer:
$-2x - h - 2$

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QUESTION IMAGE

Question

Explanation:

Step1: Find $f(x + h)$

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

Step3: Find the difference quotient $\frac{f(x + h)-f(x)}{h}$

Answer: