Answer
See below.
Work Step by Step
General formula for average rate of change from x to y: $\frac{f(y)-f(x)}{y-x}.$ Hence here:
a) $\frac{f(2)-f(1)}{2-1}=\frac{(8\cdot2^2-2)-(8\cdot1^2-1)}{1}=(8\cdot4-2)-(8\cdot1)-1=32-2-8+1=23.$
b) $\frac{f(1)-f(0)}{2-1}=\frac{(8\cdot1^2-1)-(8\cdot0^2-0)}{1}=(8\cdot1-1)-(8\cdot0-0)=8-1-0=7.$
c) $\frac{f(4)-f(2)}{4-2}=\frac{(8\cdot4^2-4)-(8\cdot2^2-2)}{2}=\frac{(8\cdot16-4)-(8\cdot4-2)}{2}=\frac{128-4-32+2}{2}=\frac{94}{2}=47$
