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

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

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extreme f(x)=(2cos(θ)+cos^2(θ))

extreme points

f (x) = (2 cos (θ) + cos^{2} (θ))

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

Solution steps

Find the critical points:

θ = 2 πn, θ = π + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn < θ < π + 2 πn,

Increasing

: π + 2 πn < θ < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

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

Maximum (2 πn, 3)

Plug the extreme point

x = π + 2 πn

into

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

Minimum (π + 2 πn, - 1)

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

f (x, y) = 2 x^{2} - x^{4} + 3 y^{2} - y^{3}

f (x) = 2 sin (x) cos (x)

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

f (x) = x^{2} + x y + y^{2} - 7 y + 16

f (x, y) = x^{2} + x y + y^{2} + 7 y

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