Where are the critical points of #sec x#? Precalculus Graphs of Trigonometric Functions Graphing Trigonometric Functions with Critical Points 1 Answer 1s2s2p Mar 12, 2018 #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# Answer link Related questions Where are the critical points of #tan x#? Where are the critical points of #cot x#? Where are the critical points of #csc x#? What are the critical points of #y=2 tan x# on #[0, pi^2]#? See all questions in Graphing Trigonometric Functions with Critical Points Impact of this question 5956 views around the world You can reuse this answer Creative Commons License