NMaximize

A numeric global maximum of f over a BOUNDED interval, as {value, {x -> point}} -- dense sampling plus a golden-section refinement, not an exact answer.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageNMaximize!↗

NMaximize({f, cons}, x)the numeric global maximum of f over the bounded interval cons implies, for any real-valued f (not just the exact core Maximize covers).

Typed signatures

Type	Package	Applies
(tuple<expression, expression>, list<symbol> | symbol) -> expression	analytic	always

Domain: Calculus

Details

• NMinimize's exact mirror image -- same method (201-point sampling plus a golden-section refinement, converged to a bracket width under 1e-11 relative to the interval), same requirement for an explicit bounded constraint, same declines. See its details for the full account.
• When f has more than one point attaining the same global maximum, this reports whichever the sampling grid's basin of attraction happens to land on first -- a different, equally valid witness than another correct implementation (or Wolfram's own NMaximize) might report for the same value.

Examples

Basic #

Sin(x) + Cos(2x) reaches its maximum, 9/8, at more than one point on [0, 6]

live ↗

In$\mathrm{NMaximize}(\bigl\lbrack\sin(x)+\cos(2x), x≥0∧x≤6\bigr\rbrack, x)$Out$\bigl\lbrack1.125, \bigl\lbrack\mathrm{Rule}(x, 2.888\,912\,406\,121\,017\,6)\bigr\rbrack\bigr\rbrack$

Possible issues #

Declines -- no bounded interval to search

live ↗

In$\mathrm{NMaximize}(-x^2, x)$Out$\mathrm{NMaximize}(-x^2, x)$

About

Examples	2
Checked against	Wolfram Language 2 differ
Crosswalk	Wolfram Language

See also: NMinimize, Maximize, MaxValue