What is the extreme f(x)=6sec(x) ?

The extreme f(x)=6sec(x) is Minimum(2pin,6),Maximum(pi+2pin,-6)

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extreme f(x)=6sec(x)

extreme points

f (x) = 6 sec (x)

Minimum (2 πn, 6), Maximum (π + 2 πn, - 6)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

6 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

6 sec (x) \Rightarrow y = 6

Minimum (2 πn, 6)

Plug the extreme point

x = π + 2 πn

into

6 sec (x) \Rightarrow y = - 6

Maximum (π + 2 πn, - 6)

Minimum (2 πn, 6), Maximum (π + 2 πn, - 6)

f (x) = 4 (x^{\frac{1}{5}} - 5) + 10

y = \frac{3}{x ^{2} - 49}

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

\frac{x + 7}{x ^{2} - 6 x + 8}

f (x) = \frac{2 x - 5}{x}

What is the extreme f(x)=6sec(x) ?
The extreme f(x)=6sec(x) is Minimum(2pin,6),Maximum(pi+2pin,-6)