Question

What is the average rate of change for the function f(x)= -2x^3 + x - 1 over the interval from x = 1 to x = 3?

Answer 1

Given:

The function is,

`f(x)=-2x^3+x-1`

Step-by-step explanation:

The average rate of change of function f(x) over x = a to x = b is,

`A=(f(b)-f(a))/(b-a)`

Determine the average rate of change of function f(x) = -2x^3 + x - 1.

`\begin{gathered} A=(f(3)-f(1))/(3-1) \\ =((-2\cdot(3)^3+3-1)-(-2(1)^3+1-1))/(2) \\ =((-2\cdot27+2)-(-2))/(2) \\ =(-52+2)/(2) \\ =-(50)/(2) \\ =-25 \end{gathered}`

So answer is -25.