What is the extreme f(x)=sec(x-pi/4) ?

The extreme f(x)=sec(x-pi/4) is Minimum(pi/4+2pin,1),Maximum((5pi)/4+2pin,-1)

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extreme f(x)=sec(x-pi/4)

extreme points

f (x) = sec (x - \frac{π}{4})

Minimum (\frac{π}{4} + 2 πn, 1), Maximum (\frac{5 π}{4} + 2 πn, - 1)

Solution steps

Find the critical points:

x = \frac{π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Domain of

sec (x - \frac{π}{4}) : 2 πn \leq x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{4} + 2 πn,

Increasing

: \frac{π}{4} + 2 πn < x < \frac{3 π}{4} + 2 πn,

Increasing

: \frac{3 π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn,

Decreasing

: \frac{5 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn,

Decreasing

: \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{4} + 2 πn

into

sec (x - \frac{π}{4}) \Rightarrow y = 1

Minimum (\frac{π}{4} + 2 πn, 1)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

sec (x - \frac{π}{4}) \Rightarrow y = - 1

Maximum (\frac{5 π}{4} + 2 πn, - 1)

Minimum (\frac{π}{4} + 2 πn, 1), Maximum (\frac{5 π}{4} + 2 πn, - 1)

What is the extreme f(x)=sec(x-pi/4) ?
The extreme f(x)=sec(x-pi/4) is Minimum(pi/4+2pin,1),Maximum((5pi)/4+2pin,-1)