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

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

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

extreme points

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

Maximum (2 πn, 3), Minimum (π + 2 πn, - 1)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

2 cos (x) + cos^{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) + cos^{2} (x) \Rightarrow y = 3

Maximum (2 πn, 3)

Plug the extreme point

x = π + 2 πn

into

2 cos (x) + cos^{2} (x) \Rightarrow y = - 1

Minimum (π + 2 πn, - 1)

Maximum (2 πn, 3), Minimum (π + 2 πn, - 1)

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