Answer
General shape:
Work Step by Step
Step 2
$y'=\displaystyle \sec^{2}x,\quad -\frac{\pi}{2} \lt x \lt \frac{\pi}{2}$
$y''=2\sec x\cdot(\sec x\cdot\tan x)=2\sec^{2}x\cdot\tan x$
Step 3
$y'\geq 0$ for all $ x\displaystyle \in(-\frac{\pi}{2}, \frac{\pi}{2}) \qquad$... $f$ never decreases.
Step 4
$\left[\begin{array}{cccccc}
y': & & ( & ++ & )\\
& & -\pi/2 & & \pi/2\\
y: & & & \nearrow &
\end{array}\right]$
Step 5
For concavity, $y''=0$ for $x=0,\ $
$\left[\begin{array}{cccccc}
y'': & & ( & -- & 0 & ++ & )\\
& & -\pi/2 & & 0 & \pi/2 & \\
y: & & & \cap & i.p. & \cup &
\end{array}\right]$
