What is the extreme 3cos(4x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme 3cos(4x)

extreme points

3 cos (4 x)

Maximum (\frac{π}{2} n, 3), Minimum (\frac{π}{4} + \frac{π}{2} n, - 3)

Solution steps

Find the critical points:

x = \frac{π}{2} n, x = \frac{π}{4} + \frac{π}{2} n

Domain of

3 cos (4 x) : - \infty < x < \infty

Find intervals:

Decreasing

: \frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n,

Increasing

: \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Plug the extreme point

x = \frac{π}{2} n

into

3 cos (4 x) \Rightarrow y = 3

Maximum (\frac{π}{2} n, 3)

Plug the extreme point

x = \frac{π}{4} + \frac{π}{2} n

into

3 cos (4 x) \Rightarrow y = - 3

Minimum (\frac{π}{4} + \frac{π}{2} n, - 3)

Maximum (\frac{π}{2} n, 3), Minimum (\frac{π}{4} + \frac{π}{2} n, - 3)

f (x) = (2 x - 14)^{4}

f (x) = (x - 2)^{3} + 3

- (x - 1)^{2} + 4

f (x) = 2 x 4 - x^{2}

f (x) = 9 x^{2} - x^{3} - 3

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