find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it. $f(x)=x^{2}+7x + 4$ question help: video written example submit question

Question

Accepted Answer

# Explanation:
## Step1: Find $f(x + h)$
Substitute $x+h$ into $f(x)$:
$f(x + h)=(x + h)^2+7(x + h)+4=x^{2}+2xh+h^{2}+7x + 7h+4$
## Step2: Calculate $f(x + h)-f(x)$
$$
\begin{align*}
f(x + h)-f(x)&=(x^{2}+2xh+h^{2}+7x + 7h+4)-(x^{2}+7x + 4)\
&=x^{2}+2xh+h^{2}+7x + 7h+4 - x^{2}-7x - 4\
&=2xh+h^{2}+7h
\end{align*}
$$
## Step3: Find the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}+7h}{h}\
&=\frac{h(2x + h+7)}{h}\
&=2x+h + 7
\end{align*}
$$
# Answer:
$2x+h + 7$

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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: