Absolute Extrema: Use Critical Points and Endpoints

This lesson develops the closed-interval method for finding absolute maxima and minima. It distinguishes an extremum's value, f(c), from its location, c, then states the Extreme Value Theorem with its continuity and closed-interval conditions. 1

You will learn why endpoints and interior critical points form the candidate list, including points where the derivative is undefined, and why a critical point is not automatically an extremum. 1

Two complete examples show the exam-credit workflow: check the theorem's conditions, solve for critical points, evaluate every candidate, and compare the outputs to identify the absolute maximum and minimum. 1