What is the extreme f(x)=cot(x)+tan(x) ?

The extreme f(x)=cot(x)+tan(x) is Minimum(pi/4+pin,2),Maximum((3pi)/4+pin,-2)

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extreme f(x)=cot(x)+tan(x)

extreme

Minimum (\frac{π}{4} + πn, 2), Maximum (\frac{3 π}{4} + πn, - 2)

Solution steps

Find the critical points:

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Domain of

cot (x) + tan (x) : πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Find intervals:

Decreasing

: πn < x < \frac{π}{4} + πn,

Increasing

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

Increasing

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

Decreasing

: \frac{3 π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

cot (x) + tan (x) \Rightarrow y = 2

Minimum (\frac{π}{4} + πn, 2)

Plug the extreme point

x = \frac{3 π}{4} + πn

into

cot (x) + tan (x) \Rightarrow y = - 2

Maximum (\frac{3 π}{4} + πn, - 2)

Minimum (\frac{π}{4} + πn, 2), Maximum (\frac{3 π}{4} + πn, - 2)

What is the extreme f(x)=cot(x)+tan(x) ?
The extreme f(x)=cot(x)+tan(x) is Minimum(pi/4+pin,2),Maximum((3pi)/4+pin,-2)