Question

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 $f(x)$:

$$
LATEXBLOCK0
$$

Step3: Calculate $f(3)$

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

$$
LATEXBLOCK1
$$

Step4: Calculate the average rate of change

$$
LATEXBLOCK2
$$

Answer:

$19$