What is the extreme f(x)=csc^2(x)-2/(sqrt(3))cot(x) ?

The extreme f(x)=csc^2(x)-2/(sqrt(3))cot(x) is Minimum(pi/3+pin, 2/3)

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extreme f(x)=csc^2(x)-2/(sqrt(3))cot(x)

extreme points

f (x) = csc^{2} (x) - \frac{2}{3} cot (x)

Minimum (\frac{π}{3} + πn, \frac{2}{3})

Solution steps

Find the critical points:

x = \frac{π}{3} + πn

Domain of

csc^{2} (x) - \frac{2}{3} cot (x) : πn < x < π + πn

Find intervals:

Decreasing

: πn < x < \frac{π}{3} + πn,

Increasing

: \frac{π}{3} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{3} + πn

into

csc^{2} (x) - \frac{2}{3} cot (x) \Rightarrow y = \frac{2}{3}

Minimum (\frac{π}{3} + πn, \frac{2}{3})

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

f (x) = 3 - x

f (x) = x^{2} - 14 x + 44

\frac{x}{x ^{2} + 100}

f (x) = \frac{4860}{x} + 15 x + 717904

What is the extreme f(x)=csc^2(x)-2/(sqrt(3))cot(x) ?
The extreme f(x)=csc^2(x)-2/(sqrt(3))cot(x) is Minimum(pi/3+pin, 2/3)