What is the extreme f(x)=2cos(x)+sin^2(x) ?

The extreme f(x)=2cos(x)+sin^2(x) is Maximum(2pin,2),Minimum(pi+2pin,-2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=2cos(x)+sin^2(x)

extreme points

f (x) = 2 cos (x) + sin^{2} (x)

Maximum (2 πn, 2), Minimum (π + 2 πn, - 2)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn < x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

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

Maximum (2 πn, 2)

Plug the extreme point

x = π + 2 πn

into

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

Minimum (π + 2 πn, - 2)

Maximum (2 πn, 2), Minimum (π + 2 πn, - 2)

What is the extreme f(x)=2cos(x)+sin^2(x) ?
The extreme f(x)=2cos(x)+sin^2(x) is Maximum(2pin,2),Minimum(pi+2pin,-2)