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**[SOLVED] minimum and maximum values**

An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle [tex]\vartheta[/tex] with the plane, then the magnitude of the force is

F= Z(W)/Z sin [tex]\vartheta[/tex] + cos [tex]\vartheta[/tex]

Where Z is a positive constant called the coeffecient of friction where 0< Z<[tex]\pi[/tex]/2.

Show that F is minimized when tan [tex]\vartheta[/tex] =Z

The theorem's I am allowed to use:

The extreme value theorem

Fermat's theorem

I don't really understand what the problem is asking me. What do they mean by F is minimized? Maybe if I knew that I could do it.