find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\
eq0$, for the function below.
$f(x)=5x^{2}-5x + 2$
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)=5x^{2}-5x + 2 $:
$$
\begin{align*}
f(x + h)&=5(x + h)^{2}-5(x + h)+2\
&=5(x^{2}+2xh+h^{2})-5x-5h + 2\
&=5x^{2}+10xh+5h^{2}-5x-5h + 2
\end{align*}
$$
## Step2: Calculate $ f(x + h)-f(x) $
$$
\begin{align*}
f(x + h)-f(x)&=(5x^{2}+10xh+5h^{2}-5x-5h + 2)-(5x^{2}-5x + 2)\
&=5x^{2}+10xh+5h^{2}-5x-5h + 2-5x^{2}+5x - 2\
&=10xh+5h^{2}-5h
\end{align*}
$$
## Step3: Compute $ \frac{f(x + h)-f(x)}{h} $
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{10xh+5h^{2}-5h}{h}\
&=\frac{h(10x + 5h-5)}{h}\
&=10x+5h - 5
\end{align*}
$$

# Answer:
$10x + 5h-5$

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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: