What is the extreme f(x)=sec^2(x)-2sqrt(3)tan(x) ?

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

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extreme f(x)=sec^2(x)-2sqrt(3)tan(x)

extreme points

f (x) = sec^{2} (x) - 23 tan (x)

Minimum (\frac{π}{3} + πn, - 2)

Solution steps

Find the critical points:

x = \frac{π}{3} + πn

Domain of

sec^{2} (x) - 23 tan (x) : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Find intervals:

Decreasing

: πn \leq x < \frac{π}{3} + πn,

Increasing

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

Decreasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{3} + πn

into

sec^{2} (x) - 23 tan (x) \Rightarrow y = - 2

Minimum (\frac{π}{3} + πn, - 2)

f (x) = 4 x^{3} - 12 x^{2} - 96 x + 9

f (x) = 4 x^{3} - 12 x^{2} - 96 x + 7

f (x, y) = - 25 x^{2} + 250 x - y^{2} + 8 y - 637

f (x, y) = 5 x^{2} y - 5 x y^{3} + 4 y^{3}

f (x) = 12 x - 6

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