1. ## 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 .

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

$\frac{dF}{d\theta} = 0$ 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 $F$.