Minimize Command

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This command differs among variants of English:

  • Minimize (US)

  • Minimise (UK + Aus)
Minimize( <Dependent number>, <Free number> )

Calculates the free number which gives the minimal value of the dependent number. The free number must be a slider and the slider interval will be used as the search interval. The relationship should be continuous and have only one local minimum in the interval. If the construction is complicated, this command might return ? to avoid using too much processor time.

Let a be a slider in [0,10] and t1 the right triangle with vertices C = (a, 0), A = (0, 0) and B = (0,10 - a). Minimize(t1, a) gives 0, the value of a that minimizes the area of t1 (when the triangle degenerates into a segment).

Minimize( <Dependent Number>, <Point on Path> )

Calculates the position of the point which gives the minimal value of the dependent number. The point must be a point on a path and the path will be used as the search interval. The relationship should be continuous and have only one local minimum point in the interval. If the construction is complicated, this command might return ? to avoid using too much processor time.

Let c be a circle, C a point on it and D a point outside the circle. If f = Segment(C,D) then Minimize(f,C) creates the point on c having minimum distance from D.

See also Maximize command.