Question

find the average rate of change on the interval.
h(x)=5x^{2}-5 on 0,5
question help: video ebook written example

Explanation:

Step1: Recall the average - rate - of - change formula

The average rate of change of a function $y = h(x)$ on the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 0$, $b = 5$, and $h(x)=5x^{2}-5$.

Step2: Calculate $h(5)$

Substitute $x = 5$ into $h(x)$: $h(5)=5\times5^{2}-5=5\times25 - 5=125 - 5=120$.

Step3: Calculate $h(0)$

Substitute $x = 0$ into $h(x)$: $h(0)=5\times0^{2}-5=- 5$.

Step4: Calculate the average rate of change

Using the formula $\frac{h(5)-h(0)}{5 - 0}$, we substitute the values of $h(5)$ and $h(0)$: $\frac{120-(-5)}{5}=\frac{120 + 5}{5}=\frac{125}{5}=25$.

Answer:

25