Question

Find the absolute maximum and absolute minimum of the function f(x) = (2x^(5/2))/5 - (2x^(3/2))/3 - 6 over the interval [0, 4].

Answer 1

To find the absolute maximum and absolute minimum of a function, use the first and second derivative tests.

Step-by-step explanation:

To find the absolute maximum and absolute minimum of the function f(x) = (2x5/2)/5 - (2x3/2)/3 - 6 over the interval [0, 4], we can use the first and second derivative tests.

1. Find the critical points by setting the derivative equal to zero and solving for x.
2. Evaluate f(x) at the critical points and the endpoints of the interval.
3. The largest value is the absolute maximum, and the smallest value is the absolute minimum.

By performing these steps, we can determine the absolute maximum and absolute minimum of the given function.