Where are the critical points of $sec x$ ?

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Answer 1 · 2018-03-12T12:26:29

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

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 $n∈ZZ$

Where are the critical points of sec xsec x?