review for exam 1 over chapters 2 and 3
score: 19/32 answered: 21/32
question 22
for the function ( f(x)=5 x^{2}-3 x ), evaluate and simplify.
( \frac{f(x+h)-f(x)}{h}= )
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Question

Accepted Answer

# Explanation:
## Step1: Find $ f(x + h) $
Substitute $ x+h $ into $ f(x)=5x^{2}-3x $.
$$
\begin{align*}
f(x + h)&=5(x + h)^{2}-3(x + h)\
&=5(x^{2}+2xh+h^{2})-3x - 3h\
&=5x^{2}+10xh+5h^{2}-3x - 3h
\end{align*}
$$
## Step2: Calculate $ f(x + h)-f(x) $
$$
\begin{align*}
f(x + h)-f(x)&=(5x^{2}+10xh+5h^{2}-3x - 3h)-(5x^{2}-3x)\
&=5x^{2}+10xh+5h^{2}-3x - 3h - 5x^{2}+3x\
&=10xh+5h^{2}-3h
\end{align*}
$$
## Step3: Find $ \frac{f(x + h)-f(x)}{h} $
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{10xh+5h^{2}-3h}{h}\
&=\frac{h(10x + 5h-3)}{h}\
&=10x + 5h-3\quad(h
eq0)
\end{align*}
$$

# Answer:
$10x + 5h-3$

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QUESTION IMAGE

Question

Explanation:

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

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

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

Answer: