determine the average rate of change of the function on the given interval. express your answer in exact…

determine the average rate of change of the function on the given interval. express your answer in exact simplest form. f(x)=x² - 2 part 1 of 3 instructor note remember, average rate of change on the interval a,b means to find the average rate of change from x=a to x=b. (a) on -2,0 the average rate of change of the function is . part 2 of 3 (b) on 3,4 the average rate of change of the function is . part 3 of 3 (c) on 4,6 the average rate of change of the function is .

determine the average rate of change of the function on the given interval. express your answer in exact simplest form. f(x)=x² - 2 part 1 of 3 instructor note remember, average rate of change on the interval a,b means to find the average rate of change from x=a to x=b. (a) on -2,0 the average rate of change of the function is . part 2 of 3 (b) on 3,4 the average rate of change of the function is . part 3 of 3 (c) on 4,6 the average rate of change of the function is .

Answer

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate for part (a)

For $f(x)=x^{2}-2$ on $[-2,0]$, $a=-2$, $b = 0$. First, find $f(-2)$ and $f(0)$. $f(-2)=(-2)^{2}-2=4 - 2=2$, $f(0)=0^{2}-2=-2$. Then $\frac{f(0)-f(-2)}{0-(-2)}=\frac{-2 - 2}{2}=\frac{-4}{2}=-2$.

Step3: Calculate for part (b)

For the interval $[3,4]$, $a = 3$, $b = 4$. $f(3)=3^{2}-2=9 - 2=7$, $f(4)=4^{2}-2=16 - 2=14$. Then $\frac{f(4)-f(3)}{4 - 3}=\frac{14 - 7}{1}=7$.

Step4: Calculate for part (c)

For the interval $[4,6]$, $a = 4$, $b = 6$. $f(4)=4^{2}-2=14$, $f(6)=6^{2}-2=36 - 2=34$. Then $\frac{f(6)-f(4)}{6 - 4}=\frac{34 - 14}{2}=\frac{20}{2}=10$.

Answer:

(a) -2 (b) 7 (c) 10