sections 1.3 - 1.4
score: 5/21 answered: 5/21
question 6
given ( f(x)=2 x^{2}+7 ), find the average rate of change of ( f(x) ) on the interval ( 9,9+h ). your answer will be an expression involving ( h ).
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# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 9$ and $b=9 + h$, so we need to find $f(9 + h)$ and $f(9)$ first.
## Step2: Calculate $f(9 + h)$
Substitute $x=9 + h$ into $f(x)=2x^{2}+7$.
$$
\begin{align*}
f(9 + h)&=2(9 + h)^{2}+7\
&=2(81+18h+h^{2})+7\
&=162 + 36h+2h^{2}+7\
&=2h^{2}+36h + 169
\end{align*}
$$
## Step3: Calculate $f(9)$
Substitute $x = 9$ into $f(x)=2x^{2}+7$.
$$
\begin{align*}
f(9)&=2\times9^{2}+7\
&=2\times81+7\
&=162 + 7\
&=169
\end{align*}
$$
## Step4: Compute the average rate of change
$$
\begin{align*}
\frac{f(9 + h)-f(9)}{(9 + h)-9}&=\frac{(2h^{2}+36h + 169)-169}{h}\
&=\frac{2h^{2}+36h}{h}\
&=\frac{h(2h + 36)}{h}\
&=2h+36\quad(h
eq0)
\end{align*}
$$

# Answer:
$2h + 36$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(f(9 + h)\)

Step3: Calculate \(f(9)\)

Step4: Compute the average rate of change

Answer: