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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme

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)

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