find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it. $f(x)=3x^{2}+6x$ the difference quotient is $square$. (simplify your answer. do not factor.)

Question

Accepted Answer

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

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QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

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

Step3: Calculate the difference quotient

Answer: