find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\
eq0$, for the function below.
$f(x)=-x^{2}+5x - 5$
simplify your answer as much as possible.
$\frac{f(x + h)-f(x)}{h}=\square$

Question

Accepted Answer

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

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QUESTION IMAGE

Question

Explanation:

Step1: Find \( f(x + h) \)

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

Step3: Compute \( \frac{f(x + h)-f(x)}{h} \)

Answer: