when ...
is a critical value
... I'll leave it for you to verify that it is the angle that yields the minimum value of .
A woman pulls a sled which, together with its load, has a mass of kg. If her arm makes an angle of with her body (assumed vertical) and the coefficient of friction (a positive constant) is , the least force, , she must exert to move the sled is given by If , find the maximum and minimum values of for .