What is the extreme sec(x) ?

The extreme sec(x) is Minimum(2pin,1),Maximum(pi+2pin,-1)

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extreme sec(x)

extreme points

sec (x)

Minimum (2 πn, 1), Maximum (π + 2 πn, - 1)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

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

Find intervals:

Increasing

: 2 πn < x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < π + 2 πn,

Decreasing

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

Decreasing

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

Plug the extreme point

x = 2 πn

into

sec (x) \Rightarrow y = 1

Minimum (2 πn, 1)

Plug the extreme point

x = π + 2 πn

into

sec (x) \Rightarrow y = - 1

Maximum (π + 2 πn, - 1)

Minimum (2 πn, 1), Maximum (π + 2 πn, - 1)

What is the extreme sec(x) ?
The extreme sec(x) is Minimum(2pin,1),Maximum(pi+2pin,-1)