Question

If f(x)=x3-x,what is the average rate of change of f(x) over the interval [1, 5]?

Answer 1

f(1)=0,f(5)=120

{average rate of change of f(x) over the interval [1, 5] } = [f(5)-f(1)]/(5-1)=120/4=30

Answer 2

The average rate of change in the interval [1,5] is 30.

Explanation:

The function is given by
`f(x)=x^3-x`

Then, we have that,

`f(5)=5^3-5\\\\f(5)=125-5\\\\f(5)=120`

Also, we have,

`f(1)=1^3-1\\\\f(1)=1-1\\\\f(1)=0`

So, the average rate of change over the interval [1,5] will be,

`Rate=(f(5)-f(1))/(5-1)\\\\Rate=(120-0)/(4)\\\\Rate=(120)/(4)\\\\Rate=30`

Thus, the average rate of change in the interval [1,5] is 30.