Single Variable Calculus, Chapter 4, 4.7, Section 4.7, Problem 40

Suppose that $\displaystyle F = \frac{\mu W}{\mu \sin \theta + \cos \theta}$. For what value of $\theta$ is $F$ smallest. Assuming that other quantities are constants.

Taking the derivative of $F$ with respect to $\theta$, we get...
$\displaystyle F' = \frac{(\mu \sin \theta + \cos \theta) (0) - (\mu W) (\mu \cos \theta - \sin \theta)}{(\mu \sin \theta + \cos \theta)^2}$
when $F'=0$


$
\begin{equation}
\begin{aligned}
0 &= - (\mu W) (\mu \cos \theta - \sin \theta)\\
\\
0 &= \mu \cos \theta - \sin \theta\\
\\
\sin \theta &= \mu \cos \theta\\
\\
\frac{\sin \theta}{\cos \theta} &= \mu\\
\\
\tan \theta &= \mu
\end{aligned}
\end{equation}
$


Therefore, $F$ is smallest when $\theta = \tan^{-1}[\mu]$