17. -/1 points let f(x)=-x^{2}+4x - 7. find and simplify the difference quotient, $\frac{f(x + h)-f(x)}{h}$. resources ebook

Question

Accepted Answer

# Explanation:
## Step1: Find $f(x + h)$
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=-(x + h)^2+4(x + h)-7\
&=-(x^{2}+2xh+h^{2})+4x + 4h-7\
&=-x^{2}-2xh - h^{2}+4x + 4h-7
\end{align*}
$$
## Step2: Calculate $f(x + h)-f(x)$
$$
\begin{align*}
f(x + h)-f(x)&=(-x^{2}-2xh - h^{2}+4x + 4h-7)-(-x^{2}+4x - 7)\
&=-x^{2}-2xh - h^{2}+4x + 4h-7 + x^{2}-4x + 7\
&=-2xh - h^{2}+4h
\end{align*}
$$
## Step3: Calculate $\frac{f(x + h)-f(x)}{h}$
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{-2xh - h^{2}+4h}{h}\
&=\frac{h(-2x - h + 4)}{h}\
&=-2x - h+4
\end{align*}
$$
# Answer:
$-2x - h + 4$

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QUESTION IMAGE

Question

Explanation:

Step1: Find $f(x + h)$

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

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

Answer: