Answer
$a) 23 \\ b) 7 \\ c) 47$
Work Step by Step
The general formula for the average rate of change from $a$ to $b$ is:
$avg=\dfrac{f(b)-f(a)}{b-a}$
We use this formula to calculate the average rate of change for the given points:
$a)\displaystyle \frac{f(2)-f(1)}{2-1}=\frac{(8(2)^2-2)-(8(1)^2-1)}{1}=(8\cdot4-2)-(8(1))-1\\=23 \\ b) \displaystyle \frac{f(1)-f(0)}{2-1}=\frac{(8\cdot1^2-1)-(8(0)^2-0)}{1}=(8\cdot1-1)-(8(0)-0)\\=7 \\ c) \displaystyle \frac{f(4)-f(2)}{4-2}=\frac{(8\cdot4^2-4)-(8(2)^2-2)}{2}=\frac{(8(16)-4)-(8(4)-2)}{2}=\frac{128-4-32+2}{2}\\=47$
