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:
\(A(x) = \frac{f(b)-f(a)}{b-a}\) ....[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;
\(A(x) = \frac{f(5)-f(1)}{5-1}\)
⇒\(A(x) = \frac{120-0}{4}\)
⇒\(A(x) = \frac{120}{4}=30\)
Therefore, the average rate of change of f(x) over the interval [1, 5] is, 30
