Question

If ,f(x)=x^3-x what is the average rate of change of f(x) over the interval [1, 5]?

a. 29.5
b. 30
c. 43
d. 120

Answer 1

Its b.30

Explanation:

Answer 2

Option b is correct

30 is the average rate of change of f(x) over the interval [1, 5]

Explanation:

Average rate of change (A(x)) of f(x) over interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)` ....[1]

As per the statement:

Given the function:

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

We have to find the average rate of change of f(x) over the interval [1, 5].

At x = 1

then;

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

At x= 5

then;

`f(1) = 5^3-5 =125-5 =120`

Substitute these given values in [1] we have;

`A(x) = (f(5)-f(1))/(5-1)`

⇒
`A(x) = (120-0)/(4)`

⇒
`A(x) = (120)/(4)=30`

Therefore, the average rate of change of f(x) over the interval [1, 5] is, 30