What is the extreme f(x)=4sec(x) ?

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

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extreme f(x)=4sec(x)

extreme points

f (x) = 4 sec (x)

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

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn < x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < π + 2 πn,

Decreasing

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

Decreasing

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

Plug the extreme point

x = 2 πn

into

4 sec (x) \Rightarrow y = 4

Minimum (2 πn, 4)

Plug the extreme point

x = π + 2 πn

into

4 sec (x) \Rightarrow y = - 4

Maximum (π + 2 πn, - 4)

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

f (x, y) = y x^{2} - 3 x y e^{- x y}

f (x, y) = x^{3} - 9 x y - 4 y^{2}

y = 4 - 6 x^{2}

\frac{x ^{2} + 2}{x - 3}

f (x) = 5 + \frac{48}{x} + 3 x^{2}

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