Question

Use the table below of the function f(x) = x4 − 2x3 to answer this question: x f(x) −1 3 0 0 1 −1 2 0 3 27 What is the average rate of change from x = −1 to x = 1?

Answer 1

The average rate of change is
`-2`

Explanation:

The given function is

`f(x)=x^4-2x^3`

The average rate of change of
`f(x)=x^4-2x^3`

from
`x=-1` to
`x=1` is the slope of the secant line joining the points.

`(-1,f(-1))` and
`(1,f(1))`

From the table,

`f(-1)=3` and
`f(1)=-1`.

Average Rate of Change

`=(f(1)-f(-1))/(1--1)`

`=(-1-3)/(1--1)`

`=(-4)/(2)`

`=-2`

Answer 2

`f(x) = x^4 - 2x^3`

the average rate of change from x = −1 to x = 1

When x= -1 , f(-1)= 3

When x= 1, f(1)= -1

Average rate of change =
`(f(b)-f(a))/(b-a)`

a=-1 , b= 1

Average rate of change =
`(f(1)-f(-1))/(1-(-1))`

Plug in the values of f(-1) and f(1)

=
`(-1-3)/(1-(-1))`

=
`(-4)/(2) = -2`

Average rate of change = -2