Question

(a) Determine the net change between the given values of the variable

(b) Determine the average rate of change between the given values of the variable

Answer 1

Part (a)

`f(3)=5-3(3)^2=-22 \\ \\ f(3+h)=5-3(3+h)^2 \\ \\ =5-3(h^2 +6h+9) \\ \\ =5-3h^2 -18h-27 \\ \\ =-3h^2-18h-22 \\ \\ f(3+h)-f(3)=(-3h^2-18h-22)-(-22)=\boxed{3h^2 +18h}`

Part (b)

`(f(3+h)-f(3))/((3+h)-3) \\ \\ =(-3h^2-18h)/(h) \\ \\ =\boxed{-3h-18}`