Final answer:
To find the absolute maximum and minimum values of the function f(x) = x² - x - 4 on the interval [0, 4], we evaluate the function at the critical points and endpoints of the interval. The absolute maximum value is 8 (at x = 4) and the absolute minimum value is -4 (at x = 0).
Step-by-step explanation:
To find the absolute maximum and minimum values of the function f(x) = x² - x - 4 on the interval [0, 4], we need to evaluate the function at the critical points. First, we find the derivative of f(x) using the power rule: f'(x) = 2x - 1. Then, we set the derivative equal to 0 to find the critical points: 2x - 1 = 0. Solving for x, we get x = 1/2. Next, we evaluate f(x) at the endpoints of the interval: f(0) = -4 and f(4) = 8. Finally, we compare the function values at the critical points and endpoints to determine the absolute maximum and minimum values. In this case, the absolute maximum value is 8 (at x = 4) and the absolute minimum value is -4 (at x = 0).