What is the extreme 1/(1+cos(x)) ?

The extreme 1/(1+cos(x)) is Minimum(2pin, 1/2)

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extreme 1/(1+cos(x))

extreme points

\frac{1}{1 + cos ( x )}

Minimum (2 πn, \frac{1}{2})

Solution steps

Find the critical points:

x = 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

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

Minimum (2 πn, \frac{1}{2})

f (x) = \frac{x ^{8}}{x ^{2} + 6}

ln (x^{2})

(- 5.1, - 2), (1.4, 1.7)

f (x) = x 7 - x

x (x - 1)

What is the extreme 1/(1+cos(x)) ?
The extreme 1/(1+cos(x)) is Minimum(2pin, 1/2)