What is the extreme f(x)=2sec(1/2 x) ?

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

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extreme f(x)=2sec(1/2 x)

extreme points

f (x) = 2 sec (\frac{1}{2} x)

Minimum (4 πn, 2), Maximum (2 π + 4 πn, - 2)

Solution steps

Find the critical points:

x = 4 πn, x = 2 π + 4 πn

Domain of

2 sec (\frac{1}{2} x) : 4 πn \leq x < π + 4 πn or π + 4 πn < x < 3 π + 4 πn or 3 π + 4 πn < x < 4 π + 4 πn

Find intervals:

Increasing

: 4 πn < x < π + 4 πn,

Increasing

: π + 4 πn < x < 2 π + 4 πn,

Decreasing

: 2 π + 4 πn < x < 3 π + 4 πn,

Decreasing

: 3 π + 4 πn < x < 4 π + 4 πn

Plug the extreme point

x = 4 πn

into

2 sec (\frac{1}{2} x) \Rightarrow y = 2

Minimum (4 πn, 2)

Plug the extreme point

x = 2 π + 4 πn

into

2 sec (\frac{1}{2} x) \Rightarrow y = - 2

Maximum (2 π + 4 πn, - 2)

Minimum (4 πn, 2), Maximum (2 π + 4 πn, - 2)

f (x) = \frac{2 x - 7}{3}

f (x) = 3 x^{2} + 6 x

lo g_{3} (x)

\frac{1}{x} + 1

f (x) = \frac{x - 1}{x ^{2} - 3 x - 4}

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