Final answer:
To find the absolute maximum and minimum values of a function on an interval, find the critical points and compare them to the endpoints.
Step-by-step explanation:
To find the absolute maximum and minimum values of a function on a given interval, you can follow these steps:
- Find the critical points of the function by setting the derivative equal to zero and solving for x.
- Check the endpoints of the interval to see if they have higher or lower values than the critical points.
- Compare the values of the critical points and the endpoints to determine the absolute maximum and minimum.
For example, let's say we have the function f(x) = x^2 on the interval [0, 3]. The critical point is x = 0 and the endpoints are x = 0 and x = 3. Evaluating the function at these points, we find that f(0) = 0, f(3) = 9. Therefore, the absolute maximum is 9 at x = 3 and the absolute minimum is 0 at x = 0.