find the average rate of change of h(x)=x² - 5x + 2 from x = 2 to x = 5. simplify your answer as much as…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ from $x = a$ to $x = b$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 2$, $b = 5$, and $h(x)=x^{2}-5x + 2$.

Step2: Calculate $h(5)$

Substitute $x = 5$ into $h(x)$: $h(5)=5^{2}-5\times5 + 2=25-25 + 2=2$.

Step3: Calculate $h(2)$

Substitute $x = 2$ into $h(x)$: $h(2)=2^{2}-5\times2 + 2=4-10 + 2=-4$.

Step4: Calculate the average rate of change

$\frac{h(5)-h(2)}{5 - 2}=\frac{2-(-4)}{3}=\frac{2 + 4}{3}=\frac{6}{3}=2$.

Answer:

2