Find the critical points of the following functions on the given intervals. Identify the absolute maximum and absolute minimum values (if they exist).
ƒ(x) = 4x¹⸍² - x⁵⸍² on [0, 4]

Verified step by step guidance

1. First, find the derivative of the function ƒ(x) = 4x^(1/2) - x^(5/2) using the power rule. The power rule states that if ƒ(x) = x^n, then ƒ'(x) = n*x^(n-1).
2. Set the derivative equal to zero to find the critical points. This involves solving the equation ƒ'(x) = 0.
3. Evaluate the derivative at the endpoints of the interval [0, 4] to find the values of the function at these points.
4. Determine the values of the function at the critical points found in step 2 and compare them with the values from step 3.
5. Identify the absolute maximum and minimum values by comparing all the values obtained in steps 3 and 4.