Question

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

Explanation:

Step1: Define average rate formula

The average rate of change of a function $h(x)$ from $x=a$ to $x=b$ is $\frac{h(b)-h(a)}{b-a}$.

Step2: Calculate $h(2)$

Substitute $x=2$ into $h(x)$:
$h(2)=(2)^2 -5(2)+2=4-10+2=-4$

Step3: Calculate $h(5)$

Substitute $x=5$ into $h(x)$:
$h(5)=(5)^2 -5(5)+2=25-25+2=2$

Step4: Compute average rate

Substitute values into the formula:
$\frac{h(5)-h(2)}{5-2}=\frac{2-(-4)}{3}=\frac{6}{3}=2$

Answer:

2