What is the extreme 2cos^2(x) ?

The extreme 2cos^2(x) is Maximum(pin,2),Minimum(pi/2+pin,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme 2cos^2(x)

extreme points

2 cos^{2} (x)

Maximum (πn, 2), Minimum (\frac{π}{2} + πn, 0)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

2 cos^{2} (x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn < x < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

2 cos^{2} (x) \Rightarrow y = 2

Maximum (πn, 2)

Plug the extreme point

x = \frac{π}{2} + πn

into

2 cos^{2} (x) \Rightarrow y = 0

Minimum (\frac{π}{2} + πn, 0)

Maximum (πn, 2), Minimum (\frac{π}{2} + πn, 0)

f (x, y) = 4 x^{2} + y^{2} + 1

f (x) = 5 e^{x^{2} - 10 x}

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

- 3 x + ln (x)

f (x) = 52 (70 - x)

What is the extreme 2cos^2(x) ?
The extreme 2cos^2(x) is Maximum(pin,2),Minimum(pi/2+pin,0)