Built-in Mathematica Symbol

FindMaxValue

FindMaxValue[f, x]
gives the value at a local maximum of f.

FindMaxValue[f, {x, x₀}]
gives the value at a local maximum of f, found by a search starting from the point x=x₀.

FindMaxValue[f, {{x, x₀}, {y, y₀}, ...}]
gives the value at a local maximum of a function of several variables.

FindMaxValue[{f, cons}, {{x, x₀}, {y, y₀}, ...}]
gives the value at a local maximum subject to the constraints cons.

FindMaxValue[{f, cons}, {x, y, ...}]
starts from a point within the region defined by the constraints.

If the starting point for a variable is given as a list, the values of the variable are taken to be lists with the same dimensions.

FindMaxValue first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.

FindMaxValue has attribute HoldAll, and effectively uses Block to localize variables.

FindMaxValue[f, {x, x₀, x₁}] searches for a local maximum in f using x₀ and x₁ as the first two values of x, avoiding the use of derivatives.

FindMaxValue[f, {x, x₀, x_min, x_max}] searches for a local maximum, stopping the search if x ever gets outside the range x_min to x_max.

Except when f and cons are both linear, the results found by FindMaxValue may correspond only to local, but not global, maxima.

For linear f and cons, xIntegers can be used to specify that a variable can take on only integer values.

Find a maximum value of a univariate function:

Find a maximum value of a multivariate function:

Find the maximum value of a function subject to constraints: