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

Answer 1

See below.

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

#((f(x,y),x,y,"type"),(0,-pi,-pi,"minimum"),(0,0,0,"minimum"),(0,pi,pi,"minimum"))#

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

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Answer 2

Christopher Allers

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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