Where are the critical points of #sec x#?

1 Answer
Mar 12, 2018

Answer:

#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#