Question

find the average rate of change of $h(x) = 2x^2 - 7x$ from $x = 2$ to $x = 6$. 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 $\frac{h(b)-h(a)}{b-a}$.
Here, $a=2$, $b=6$, $h(x)=2x^2-7x$.

Step2: Calculate $h(6)$

Substitute $x=6$ into $h(x)$:
$h(6)=2(6)^2-7(6)=2(36)-42=72-42=30$

Step3: Calculate $h(2)$

Substitute $x=2$ into $h(x)$:
$h(2)=2(2)^2-7(2)=2(4)-14=8-14=-6$

Step4: Compute average rate

Substitute values into the formula:
$\frac{h(6)-h(2)}{6-2}=\frac{30-(-6)}{4}=\frac{36}{4}=9$

Answer:

9