section 3.3 homework\nscore: 0/9 answered: 1/9\n× question 1\nscore on last try: 0 of 1 pts. see details for…

section 3.3 homework\nscore: 0/9 answered: 1/9\n× question 1\nscore on last try: 0 of 1 pts. see details for more.\n> next question ↺ get a similar question you can retry this question below\nfind the average rate of change of the function f(x)=2x² + 3x + 2, on the interval x ∈ 3,5.\naverage rate of change = 18 ×\ngive exact answer!

section 3.3 homework\nscore: 0/9 answered: 1/9\n× question 1\nscore on last try: 0 of 1 pts. see details for more.\n> next question ↺ get a similar question you can retry this question below\nfind the average rate of change of the function f(x)=2x² + 3x + 2, on the interval x ∈ 3,5.\naverage rate of change = 18 ×\ngive exact answer!

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:

$19$