Question

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1.

Answer 1

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1.

Answer 2

The rate is change is 5.

Explanation:

Given :
`f(x) = x^4 + 3x^3 -5x^2 + 2x-2`

To find : Calculate the average rate of change for the function from x = -1 to x = 1 ?

Solution :

The rate of change of function from a to b is given by,

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

Here,
`f(x) = x^4 + 3x^3 -5x^2 + 2x-2` and a=-, b=1

`f(1) = 1^4 + 3(1)^3 -5(1)^2 + 2(1)-2`

`f(1) =1+3-5+ 2-2`

`f(1) =-1`

`f(-1) = (-1)^4 + 3(-1)^3 -5(-1)^2 + 2(-1)-2`

`f(-1) =1-3-5-2-2`

`f(-1) =-11`

Substitute in the formula,

`r=(-1-(-11))/(1-(-1))`

`r=(10)/(2)`

`r=5`

Therefore, the rate is change is 5.