What is the critical sec(x) ?

The critical sec(x) is x=2pin,x=pi+2pin

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critical sec(x)

critical points

sec (x)

x = 2 πn, x = π + 2 πn

Solution steps

sec (x)

Find where

f^{'} (x)

is equal to zero or undefined

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Identify critical points not in

f (x)

domain

Domain of

sec (x) : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

sec (x)

is not defined at

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

, therefore:

x = 2 πn, x = π + 2 πn

f (x) = \frac{( x - 2 ) ^{2}}{x - 4}

(3.15) (13.3)

f (x) = \frac{x ^{2}}{2}

f (x) = \frac{8}{9} cos (\frac{π x}{3})

x^{2} + 5 x + 6