MaxValue

The global maximum VALUE of f -- Maximize's value alone, without the witnessing point.

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

MaxValue(f, x)the global maximum of f over its own natural domain.

MaxValue({f, cons}, x)the global maximum of f restricted to a simple interval constraint cons.

Typed signatures

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

Domain: Calculus

Details

• A projection of Maximize onto just the value -- same scope, same machinery; see Minimize's details for the full account.
• The one case this covers that Maximize itself declines -- Sin/Cos of an affine argument, unconstrained -- because a value alone doesn't need a witnessing point Wolfram's own choice of (among infinitely many) isn't reproducible here. Its exact amplitude, +-1, is well defined regardless.

Examples

Basic #

A downward parabola's vertex value

live ↗

In$\mathrm{MaxValue}(-x^2+4x-1, x)$Out$3$

The maximum of the downward parabola is $\frac{49}{8}$

live ↗

In$\mathrm{MaxValue}(-2x^2-3x+5, x)$Out$\frac{49}{8}$

Scope #

Sin's exact maximum value, 1 -- Maximize itself would decline this (no reproducible point)

live ↗

In$\mathrm{MaxValue}(\sin(x), x)$Out$1$

An odd-degree polynomial is unbounded above

live ↗

In$\mathrm{MaxValue}(x^3, x)$Out$∞$

About

Examples	4
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language

See also: Maximize, MinValue, Minimize