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

The extreme f(x)=2-2cos(x) is Minimum(2pin,0),Maximum(pi+2pin,4)

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extreme f(x)=2-2cos(x)

extreme points

f (x) = 2 - 2 cos (x)

Minimum (2 πn, 0), Maximum (π + 2 πn, 4)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

2 - 2 cos (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

2 - 2 cos (x) \Rightarrow y = 0

Minimum (2 πn, 0)

Plug the extreme point

x = π + 2 πn

into

2 - 2 cos (x) \Rightarrow y = 4

Maximum (π + 2 πn, 4)

Minimum (2 πn, 0), Maximum (π + 2 πn, 4)

\frac{1}{x ^{2}} + \frac{4}{y ^{2}} + 4 x y^{2}

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

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

f (x) = 3 x^{5} - 5 x^{3} + 2

What is the extreme f(x)=2-2cos(x) ?
The extreme f(x)=2-2cos(x) is Minimum(2pin,0),Maximum(pi+2pin,4)