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. 1You 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
References
- 14.3: Maxima and Minima
math.libretexts.org
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