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)=x² - 9x + 5
$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute x + h into f(x):
$$
\begin{align*}
f(x + h)&=(x + h)^2-9(x + h)+5\
&=x^{2}+2xh+h^{2}-9x - 9h+5
\end{align*}
$$
## Step2: Calculate f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(x^{2}+2xh+h^{2}-9x - 9h+5)-(x^{2}-9x + 5)\
&=x^{2}+2xh+h^{2}-9x - 9h+5 - x^{2}+9x - 5\
&=2xh+h^{2}-9h
\end{align*}
$$
## Step3: Find the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-9h}{h}\
&=\frac{h(2x + h-9)}{h}\
&=2x+h - 9
\end{align*}
$$
# Answer:
$2x+h - 9$

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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

Answer: