Mathematico | Mathematico

The function $g$ is defined by

g (x) = 2 \sec (x) - \tan (x), \frac{- π}{2} < x < \frac{π}{2}

Find the exact coordinates of the minimum point.

(You do not need to justify that this is a minimum point.)

Recall that

\begin{aligned} y & = \tan (x) \\ \Rightarrow \frac{d y}{d x} & = \sec^{2} (x) \end{aligned}

and

\begin{aligned} y & = \sec (x) \\ \Rightarrow \frac{d y}{d x} & = \sec (x) \tan (x) \end{aligned}