What is the extreme sin(3X) ?

The extreme sin(3X) is Maximum(pi/6+(2pi)/3 n,1),Minimum(pi/2+(2pi)/3 n,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme sin(3X)

extreme

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 1), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 1)

Solution steps

Find the critical points:

X = \frac{π}{6} + \frac{2 π}{3} n, X = \frac{π}{2} + \frac{2 π}{3} n

Domain of

sin (3 X) : - \infty < X < \infty

Find intervals:

Increasing

: \frac{2 π}{3} n \leq X < \frac{π}{6} + \frac{2 π}{3} n,

Decreasing

: \frac{π}{6} + \frac{2 π}{3} n < X < \frac{π}{2} + \frac{2 π}{3} n,

Increasing

: \frac{π}{2} + \frac{2 π}{3} n < X < \frac{2 π}{3} + \frac{2 π}{3} n

Plug the extreme point

x = \frac{π}{6} + \frac{2 π}{3} n

into

sin (3 X) \Rightarrow y = 1

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 1)

Plug the extreme point

x = \frac{π}{2} + \frac{2 π}{3} n

into

sin (3 X) \Rightarrow y = - 1

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

Maximum (\frac{π}{6} + \frac{2 π}{3} n, 1), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 1)

What is the extreme sin(3X) ?
The extreme sin(3X) is Maximum(pi/6+(2pi)/3 n,1),Minimum(pi/2+(2pi)/3 n,-1)