What is the extreme 2-cos(x) ?

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

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extreme 2-cos(x)

extreme points

2 - cos (x)

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

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

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 - cos (x) \Rightarrow y = 1

Minimum (2 πn, 1)

Plug the extreme point

x = π + 2 πn

into

2 - cos (x) \Rightarrow y = 3

Maximum (π + 2 πn, 3)

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

f (x) = x^{\frac{1}{3}} + 2

f (x) = x^{3} - 6 x^{2} + 9 x + 6

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

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

f (x, y) = ln (y - x)

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