ArgMax

ArgMax[f, x] gives a position xmax at which f is maximized.

ArgMax[f, {x, y, ...}] gives a position {xmax, ymax, ...} at which f is maximized.

ArgMax[{f, cons}, {x, y, ...}] gives a position at which f is maximized subject to the constraints cons.

Examples

Find where a function is maximized:

ArgMax[Sin[x], x]
(* Pi/2 *)

With constraints:

ArgMax[{x + y, x^2 + y^2 <= 1}, {x, y}]
(* {1/Sqrt[2], 1/Sqrt[2]} *)

Please visit the official Wolfram Language Reference for more details.