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

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

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extreme 2cos(x)-2

extreme

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

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

2 cos (x) - 2 : - \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

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

Maximum (2 πn, 0)

Plug the extreme point

x = π + 2 πn

into

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

Minimum (π + 2 πn, - 4)

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

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