FindMinValue

FindMinValue[f,x] gives the value at a local minimum of f.

• FindMinValue[f,{x,x0}] gives the value at a local minimum of f, found by a search starting from the point x=x0.
• FindMinValue[f,{{x,x0},{y,y0},…}] gives the value at a local minimum of a function of several variables.
• FindMinValue[{f,cons},{{x,x0},{y,y0},…}] gives the value at a local minimum subject to the constraints cons.
• FindMinValue[{f,cons},{x,y,…}] starts from a point within the region defined by the constraints.

Examples

(* Find the minimum value *)
FindMinValue[x^2 + 2x + 1, x]

(* Start from a specific point *)
FindMinValue[x^4 - 3x^2 + x, {x, 0}]

(* Multivariate minimum *)
FindMinValue[(x - 1)^2 + (y - 2)^2, {{x, 0}, {y, 0}}]

Please visit the official Wolfram Language Reference for more details.