What is the extreme f(x)=cos(3x) ?

The extreme f(x)=cos(3x) is Maximum((2pi)/3 n,1),Minimum(pi/3+(2pi)/3 n,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=cos(3x)

extreme points

f (x) = cos (3 x)

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

Solution steps

Find the critical points:

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

Domain of

cos (3 x) : - \infty < x < \infty

Find intervals:

Decreasing

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

Increasing

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

Plug the extreme point

x = \frac{2 π}{3} n

into

cos (3 x) \Rightarrow y = 1

Maximum (\frac{2 π}{3} n, 1)

Plug the extreme point

x = \frac{π}{3} + \frac{2 π}{3} n

into

cos (3 x) \Rightarrow y = - 1

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

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

What is the extreme f(x)=cos(3x) ?
The extreme f(x)=cos(3x) is Maximum((2pi)/3 n,1),Minimum(pi/3+(2pi)/3 n,-1)