Absolute Extrema (Max & Min) Calculator
Evaluate absolute extrema for continuous functions over closed intervals [a, b]. Identifies interior critical numbers where the first derivative f’(x) = 0, calculates endpoint values f(a) and f(b), presents a candidate points evaluation table, and renders an interactive SVG curve visualization.
Absolute Extrema (Max / Min) Calculator
Find the global maximum and minimum of functions on a closed interval [a, b] using the Extreme Value Theorem and critical points.
Function & Interval
A continuous function f(x) on a closed interval [a, b] is guaranteed to have both an absolute maximum and minimum value occurring at either an endpoint or an interior critical point (where f'(x) = 0).
Candidate Critical Points & Endpoints Table
| Classification | x Coordinate | f(x) Value | Result |
|---|---|---|---|
| Left Endpoint | -2.0000 | -3.0000 | Interior |
| Critical Point | -1.0000 | 8.0000 | Absolute Max |
| Critical Point | 2.0000 | -19.0000 | Absolute Min |
| Right Endpoint | 3.0000 | -8.0000 | Interior |
How to Use Absolute Extrema (Max & Min) Calculator
Select Target Function
Choose from common polynomial, rational, trigonometric, or exponential calculus functions.
Set Interval [a, b]
Define the lower bound a and upper bound b of the closed interval.
Evaluate Extrema & Graph
Inspect the candidate evaluation table, global max/min coordinates, and interactive SVG plot.
Frequently Asked Questions
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