Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts

[Thomas Klemm]

From:

\(f(x) = 5 \left[\frac{1}{\sin(x)} + \frac{2}{\cos(x)} \right]\)

We get:

\(f'(x) = 5 \left[ - \frac{\cos(x)}{\sin^2(x)} + \frac{2 \sin(x)}{\cos^2(x)} \right] = 0\)

Or then after rearranging:

\(\tan^3(x) = \frac{1}{2}\)

This leads to:

\(
\begin{align*}
x &= \tan^{-1}\left(\frac{1}{\sqrt[3]{2}}\right) \\
\\
&\approx 0.670888 \\
&\approx 38.4390^\circ \\
\end{align*}
\)

Can the Prime give the exact result as well?