RegionPlot (Built-in Mathematica Symbol)

RegionPlot[pred, {x, x_min, x_max}, {y, y_min, y_max}] makes a plot showing the region in which pred is True.

Minimization and Maximization (Mathematica Tutorial)

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

MaxValue (Built-in Mathematica Symbol)

MaxValue[f, x] gives the maximum value of f with respect to x.MaxValue[f, {x, y, ...}] gives the maximum value of f with respect to x, y, .... MaxValue[{f, cons}, {x, y, ...

Assumptions and Domains (Mathematica Guide)

Mathematica has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of ...

Numerical Optimization (Mathematica Tutorial)

Searching for local minima and maxima. This finds the value of x which minimizes Γ(x), starting at x2. The last element of the list gives the value at which the minimum is ...

MinValue (Built-in Mathematica Symbol)

MinValue[f, x] gives the minimum value of f with respect to x.MinValue[f, {x, y, ...}] gives the minimum value of f with respect to x, y, .... MinValue[{f, cons}, {x, y, ...

Maximize (Built-in Mathematica Symbol)

Maximize[f, x] maximizes f with respect to x.Maximize[f, {x, y, ...}] maximizes f with respect to x, y, .... Maximize[{f, cons}, {x, y, ...}] maximizes f subject to the ...

ArgMax (Built-in Mathematica Symbol)

ArgMax[f, x] gives a position x_max at which f is maximized.ArgMax[f, {x, y, ...}] gives a position {x_max, y_max, ...} at which f is maximized.ArgMax[{f, cons}, {x, y, ...}] ...

ArgMin (Built-in Mathematica Symbol)

ArgMin[f, x] gives a position x_min at which f is minimized.ArgMin[f, {x, y, ...}] gives a position {x_min, y_min, ...} at which f is minimized.ArgMin[{f, cons}, {x, y, ...}] ...

Minimize (Built-in Mathematica Symbol)

Minimize[f, x] minimizes f with respect to x.Minimize[f, {x, y, ...}] minimizes f with respect to x, y, .... Minimize[{f, cons}, {x, y, ...}] minimizes f subject to the ...