This lesson on Absolute Maximum and Minimum is intended for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus.
Using Derivatives to Find the Absolute Maximum and Minimum Values of f(x)
• Find absolute extrema using Maximum-Minimum Principle I.
• Find absolute extrema using Maximum-Minimum Principle II.
The Extreme Value Theorem
A continuous function f(x) defined over a closed interval [a, b] must have an absolute maximum value and an absolute minimum value over [a, b].
The highest value of y in the interval [a, b] is called the absolute maximum and the lowest y value in the interval is called the absolute minimum.
This e-book shows how the absolute maximum and minimum values of a continuous function over [a, b] can be found by using calculus.