# What are the values and types of the critical points, if any, of f(x)=cos^2 x - sin^2 x ?

Apr 11, 2018

We can rewrite as

$f \left(x\right) = \cos \left(2 x\right)$

Which has first derivative

$f ' \left(x\right) = - 2 \sin \left(2 x\right)$

This has critical points at $x = \frac{\pi}{2} + \pi n$ and $x = 2 \pi n$. The crcital points at $x = \pi n$ are maximums and $x = \frac{\pi}{2} + \pi n$ are minimums.

The graph demonstrates:

graph{(cosx + sinx)(cosx - sinx) [-16.02, 16.02, -8.01, 8.01]}

Hopefully this helps!