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section 3.3 homework
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find the average rate of change of the function f(x)=2x² + 3x + 2, on the interval x ∈ 3,5.
average rate of change = 18 ×
give exact answer!

Explanation:

Step1: Recall the formula

The formula for 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 $a = 3$, $b=5$ and $f(x)=2x^{2}+3x + 2$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$:
\[

$$\begin{align*} f(5)&=2\times5^{2}+3\times5 + 2\\ &=2\times25+15 + 2\\ &=50+15 + 2\\ &=67 \end{align*}$$

\]

Step3: Calculate $f(3)$

Substitute $x = 3$ into $f(x)$:
\[

$$\begin{align*} f(3)&=2\times3^{2}+3\times3+2\\ &=2\times9 + 9+2\\ &=18+9 + 2\\ &=29 \end{align*}$$

\]

Step4: Calculate the average rate of change

\[

$$\begin{align*} \frac{f(5)-f(3)}{5 - 3}&=\frac{67-29}{2}\\ &=\frac{38}{2}\\ & = 19 \end{align*}$$

\]

Answer:

$19$