Maximum and Minimum Calculator
Find the absolute maximum and minimum values of a chosen function over a closed interval [a, b].
Function f(x)
reached at x = 2.8903
How does this calculator work?
This tool finds a function’s absolute maximum and minimum on a closed interval [a, b]. It samples 2000 evenly spaced points, evaluates the function at each, and reports the largest and smallest values together with the x-coordinates where they occur, plotting the curve with both extrema marked.
Formula
How this is calculated
Pick a function f(x) from the list and set the interval endpoints a and b. The order of a and b does not matter — the calculator uses the smaller as the lower bound and the larger as the upper bound, so the interval is always [min(a,b), max(a,b)].
The method divides the interval into N = 2000 equal subintervals, giving sample points xi = a + i·(b−a)/N for i = 0 to N. The function is evaluated at every sample point and the largest and smallest values are tracked along with the x at which they occur. By the Extreme Value Theorem a continuous function on a closed bounded interval attains both an absolute maximum and an absolute minimum, so dense sampling reliably approximates them.
Because this is a numerical sample rather than exact calculus, the reported extremum locations carry a small error on the order of one subinterval width, (b−a)/2000. For sharply peaked functions you can narrow the interval for higher resolution. Non-finite evaluations (such as overflow) are skipped, and if no finite values exist the result is undefined.
Frequently asked questions
No. The calculator automatically treats the smaller value as the lower bound and the larger as the upper bound, so [a,b] and [b,a] give the same result.
With 2000 samples the extremum x-location is accurate to roughly (b−a)/2000. Tightening the interval around a suspected extremum improves precision further.
It reports the absolute (global) maximum and minimum over the interval. A local extremum is only reported if it also happens to be the global one on that interval.
Also known as
TG we-Calculate Editorial Team. (2026). Maximum and Minimum Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/maximum-minimum-calculator
TG we-Calculate Editorial Team. "Maximum and Minimum Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/maximum-minimum-calculator.
TG we-Calculate Editorial Team, "Maximum and Minimum Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/maximum-minimum-calculator
@misc{wecalculate_maximum_minimum_calculator, title = {Maximum and Minimum Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/maximum-minimum-calculator}}, year = {2026}, note = {TG we-Calculate} }
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