Answer:
Option b is correct
30 is the average rate of change of f(x) over the interval [1, 5]
Step-by-step explanation:
Average rate of change (A(x)) of f(x) over interval [a, b] is given by:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex] ....[1]
As per the statement:
Given the function:
[tex]f(x) = x^3-x[/tex]
We have to find the average rate of change of f(x) over the interval [1, 5].
At x = 1
then;
[tex]f(1) = 1^3-1 =1-1 = 0[/tex]
At x= 5
then;
[tex]f(1) = 5^3-5 =125-5 =120[/tex]
Substitute these given values in [1] we have;
[tex]A(x) = \frac{f(5)-f(1)}{5-1}[/tex]
⇒[tex]A(x) = \frac{120-0}{4}[/tex]
⇒[tex]A(x) = \frac{120}{4}=30[/tex]
Therefore, the average rate of change of f(x) over the interval [1, 5] is, 30
