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Math Help - Optimization help?

  1. #1
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    Optimization help?

    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 .
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  2. #2
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    \frac{dF}{d\theta} = \frac{mg\mu(\mu\sin{\theta} - \cos{\theta})}{(\sin{\theta} + \mu\cos{\theta})^2}

    \frac{dF}{d\theta} = 0 when \cos{\theta} = \mu\sin{\theta} ...

    \theta  = \arctan\left(\frac{1}{\mu}\right) is a critical value

    ... I'll leave it for you to verify that it is the angle that yields the minimum value of F.
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