# How do you minimize and maximize #f(x,y)=sinx*cosy-tanx# constrained to #0<x-y<1#?

See below.

There are infinite relative minima due to the objective function periodicity. The near points to the origin are located at

Attached the feasible region plot with the level chart associated to the objective function.

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To minimize and maximize ( f(x, y) = \sin(x) \cdot \cos(y) - \tan(x) ) constrained to ( 0 < x - y < 1 ), first find the critical points of ( f(x, y) ) within the constraint region. Then, evaluate ( f(x, y) ) at these critical points and at the boundary of the constraint region. Finally, compare the values obtained to determine the minimum and maximum values of ( f(x, y) ).

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