Function Repository Resource:

# LocalMaxima

Compute the local maxima of an expression with respect to the given variables

Contributed by: Wolfram|Alpha Math Team
 ResourceFunction["LocalMaxima"][expr,x] computes the local maxima of expr with respect to x. ResourceFunction["LocalMaxima"][expr,{x,y,…}] computes the local maxima of expr with respect to multiple variables. ResourceFunction["LocalMaxima"][{expr,const},{x,y,…}] computes the local maxima of expr subject to the constraint const.

## Details and Options

ResourceFunction["LocalMaxima"] returns a list with each maximum in the form {fmax,{xxmax,yymax,}}.
The cons can contain equations, inequalities or logical combinations of these.
ResourceFunction["LocalMaxima"] only returns results when there is a bounded maximum.

## Examples

### Basic Examples (2)

Compute the local maxima of a polynomial:

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Plot them:

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### Scope (2)

Use a constraint in order to reduce the domain upon which maxima can be found:

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Compute the maxima of a function of two variables:

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### Possible Issues (1)

LocalMaxima may return duplicate results for periodic functions:

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## Publisher

Wolfram|Alpha Math Team

## Version History

• 2.0.0 – 23 March 2023
• 1.0.0 – 18 September 2020

## Author Notes

To view the full source code for GlobalMaxima, run the following code:

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