Question

warm up sheet dates: 9/22 to 9/26 name: ariel abernathy you must show all work to receive credit!!!! monday f(x)=x² find the average rate of change on each interval: on 0,3 on -2,4 tuesday

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$.

Step2: For the interval $[0,3]$

Given $f(x)=x^{2}$, then $f(3)=3^{2}=9$ and $f(0)=0^{2}=0$. So the average rate of change is $\frac{f(3)-f(0)}{3 - 0}=\frac{9 - 0}{3}=3$.

Step3: For the interval $[-2,4]$

Given $f(x)=x^{2}$, then $f(4)=4^{2}=16$ and $f(-2)=(-2)^{2}=4$. So the average rate of change is $\frac{f(4)-f(-2)}{4-(-2)}=\frac{16 - 4}{6}=2$.

Answer:

On $[0,3]$, the average rate of change is 3.
On $[-2,4]$, the average rate of change is 2.