Question

Compute the average rate of change of the function f (2) = 23 – 2? over the interval [-1, 2].

Answer 1

f(x) = x^3 - x^2 , over the interval (-1,2)

So, the rate of change will be as following:

`(f(2)-f(-1))/(2-(-1))`

at first, we will find f(2) and f(-1)

f(2) = 2^3 - 2^2 = 8 - 4 = 4

f(-1) = (-1)^3 - (-1)^2 = -1 - 1 = -2

So, the rate of change:

`(f(2)-f(-1))/(2-(-1))=(4-(-2))/(2-(-1))=(4+2)/(2+1)=(6)/(3)=2`