What is the extreme f(x)=-5sec(x) ?

The extreme f(x)=-5sec(x) is Maximum(2pin,-5),Minimum(pi+2pin,5)

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extreme f(x)=-5sec(x)

extreme points

f (x) = - 5 sec (x)

Maximum (2 πn, - 5), Minimum (π + 2 πn, 5)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

- 5 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:

Decreasing

: 2 πn < x < \frac{π}{2} + 2 πn,

Decreasing

: \frac{π}{2} + 2 πn < x < π + 2 πn,

Increasing

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

Increasing

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

Plug the extreme point

x = 2 πn

into

- 5 sec (x) \Rightarrow y = - 5

Maximum (2 πn, - 5)

Plug the extreme point

x = π + 2 πn

into

- 5 sec (x) \Rightarrow y = 5

Minimum (π + 2 πn, 5)

Maximum (2 πn, - 5), Minimum (π + 2 πn, 5)

f (x) = (1)^{3 n}

\frac{2 x + 1}{3 x ^{2} - 39 x + 108}

y = 2 x^{2} + 8 x - 1

x^{\frac{2}{3}} (x - 4)

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

What is the extreme f(x)=-5sec(x) ?
The extreme f(x)=-5sec(x) is Maximum(2pin,-5),Minimum(pi+2pin,5)