find the difference quotient $f(x)$
$f(x)=3x^{2}+7$
simplify your answer as much
$\frac{f(x + h)-f(x)}{h}=\square$

Question

Accepted Answer

# Explanation:
## Step1: Find $ f(x + h) $
Substitute $ x + h $ into $ f(x)=3x^{2}+7 $.
$$
\begin{align*}
f(x + h)&=3(x + h)^{2}+7\
&=3(x^{2}+2xh+h^{2})+7\
&=3x^{2}+6xh + 3h^{2}+7
\end{align*}
$$
## Step2: Calculate $ f(x + h)-f(x) $
$$
\begin{align*}
f(x + h)-f(x)&=(3x^{2}+6xh + 3h^{2}+7)-(3x^{2}+7)\
&=3x^{2}+6xh + 3h^{2}+7 - 3x^{2}-7\
&=6xh+3h^{2}
\end{align*}
$$
## Step3: Compute $ \frac{f(x + h)-f(x)}{h} $
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{6xh + 3h^{2}}{h}\
&=\frac{h(6x + 3h)}{h}\
&=6x+3h
\end{align*}
$$
# Answer:
$6x + 3h$

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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: