Question

verify the mean value theorem for the integral for the function f(x)= x^3 on (0,1)

Answer 1

Answer:

1/√3

Step-by-step explanation:

Given  

verify the mean value theorem for the integral for the function f(x)= x^3 on (0,1)

ANSWER  

We know that the mean value theorem says that there is at least one number c on (0, 1) such that f’(c) = 1, now f’(x) = 1.

The rate of change from x = 0 to x = 1 is f(1) – f(0) / 1 – 0 = 1/1 = 1

Now f(x) = x^3

       f’(x) = 3 x^2 = 1

                   x^2 = 1/3

                  x = 1/√3

So c = 1/√3 = 0.57 which is within the interval (0,1)