What is the extreme sin(4x) ?

The extreme sin(4x) is Maximum(pi/8+pi/2 n,1),Minimum((3pi)/8+pi/2 n,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme sin(4x)

extreme

Maximum (\frac{π}{8} + \frac{π}{2} n, 1), Minimum (\frac{3 π}{8} + \frac{π}{2} n, - 1)

Solution steps

Find the critical points:

x = \frac{π}{8} + \frac{π}{2} n, x = \frac{3 π}{8} + \frac{π}{2} n

Domain of

sin (4 x) : - \infty < x < \infty

Find intervals:

Increasing

: \frac{π}{2} n \leq x < \frac{π}{8} + \frac{π}{2} n,

Decreasing

: \frac{π}{8} + \frac{π}{2} n < x < \frac{3 π}{8} + \frac{π}{2} n,

Increasing

: \frac{3 π}{8} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Plug the extreme point

x = \frac{π}{8} + \frac{π}{2} n

into

sin (4 x) \Rightarrow y = 1

Maximum (\frac{π}{8} + \frac{π}{2} n, 1)

Plug the extreme point

x = \frac{3 π}{8} + \frac{π}{2} n

into

sin (4 x) \Rightarrow y = - 1

Minimum (\frac{3 π}{8} + \frac{π}{2} n, - 1)

Maximum (\frac{π}{8} + \frac{π}{2} n, 1), Minimum (\frac{3 π}{8} + \frac{π}{2} n, - 1)

What is the extreme sin(4x) ?
The extreme sin(4x) is Maximum(pi/8+pi/2 n,1),Minimum((3pi)/8+pi/2 n,-1)