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) = $x^{2}-8x + 3$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=(x + h)^2-8(x + h)+3\
&=x^{2}+2xh+h^{2}-8x - 8h+3
\end{align*}
$$
## Step2: Calculate f(x + h) - f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(x^{2}+2xh+h^{2}-8x - 8h+3)-(x^{2}-8x + 3)\
&=x^{2}+2xh+h^{2}-8x - 8h+3 - x^{2}+8x - 3\
&=2xh+h^{2}-8h
\end{align*}
$$
## Step3: Find the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-8h}{h}\
&=\frac{h(2x + h-8)}{h}\
&=2x+h - 8
\end{align*}
$$
# Answer:
$2x+h - 8$

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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: