What is the extreme f(x)=1+cos(x) ?

The extreme f(x)=1+cos(x) is Maximum(2pin,2),Minimum(pi+2pin,0)

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extreme f(x)=1+cos(x)

extreme points

f (x) = 1 + cos (x)

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

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

1 + cos (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

1 + cos (x) \Rightarrow y = 2

Maximum (2 πn, 2)

Plug the extreme point

x = π + 2 πn

into

1 + cos (x) \Rightarrow y = 0

Minimum (π + 2 πn, 0)

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

f (x) = x^{2} e^{- 6 x}

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

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

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

y = 2 x^{3} + 3 x^{2} - 12 x + 5

What is the extreme f(x)=1+cos(x) ?
The extreme f(x)=1+cos(x) is Maximum(2pin,2),Minimum(pi+2pin,0)