What is the extreme f(x)=3cos(x) ?

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

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extreme f(x)=3cos(x)

extreme

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

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

3 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

3 cos (x) \Rightarrow y = 3

Maximum (2 πn, 3)

Plug the extreme point

x = π + 2 πn

into

3 cos (x) \Rightarrow y = - 3

Minimum (π + 2 πn, - 3)

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

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