Question

Where are the critical points of `sec x`?

Answer 1

`x=n180^∘` where `n∈ZZ`
or
`x=(nπ)/2` where `n∈ZZ`

Explanation:

Critical points occur when `d/dx[secx]=0`

`d/dx[secx]=secxtanx=0`

`secx≠0` since that would mean `cosx=1/0=text(undefined)`

So `tanx=0`

`x=arctan(0)=0^∘,180^∘,360^∘,⋯,` `n180^∘` where `n∈ZZ`
or
`x=arctan(0)=0,π/2,π,⋯,` `(nπ)/2` where `n∈ZZ`