What is the extreme f(x)=-2sin(x) ?

The extreme f(x)=-2sin(x) is Minimum(pi/2+2pin,-2),Maximum((3pi)/2+2pin,2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-2sin(x)

extreme

Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (\frac{3 π}{2} + 2 πn, 2)

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Domain of

- 2 sin (x) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 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 = \frac{π}{2} + 2 πn

into

- 2 sin (x) \Rightarrow y = - 2

Minimum (\frac{π}{2} + 2 πn, - 2)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

- 2 sin (x) \Rightarrow y = 2

Maximum (\frac{3 π}{2} + 2 πn, 2)

Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (\frac{3 π}{2} + 2 πn, 2)

What is the extreme f(x)=-2sin(x) ?
The extreme f(x)=-2sin(x) is Minimum(pi/2+2pin,-2),Maximum((3pi)/2+2pin,2)