Question

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

Answer 1

We can rewrite as

`f(x) = cos(2x)`

Which has first derivative

`f'(x) = -2sin(2x)`

This has critical points at `x = pi/2 + pin` and `x = 2pin`. The crcital points at `x = pin` are maximums and `x = pi/2 + pin` are minimums.

The graph demonstrates:

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

Hopefully this helps!