What is the extreme 2cos((2pit)/3) ?

The extreme 2cos((2pit)/3) is Maximum(3n,2),Minimum(3/2+3n,-2)

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extreme 2cos((2pit)/3)

extreme

Maximum (3 n, 2), Minimum (\frac{3}{2} + 3 n, - 2)

Solution steps

Find the critical points:

t = 3 n, t = \frac{3}{2} + 3 n

Domain of

2 cos (\frac{2 π t}{3}) : - \infty < t < \infty

Find intervals:

Decreasing

: 3 n < t < \frac{3}{2} + 3 n,

Increasing

: \frac{3}{2} + 3 n < t < 3 + 3 n

Plug the extreme point

x = 3 n

into

2 cos (\frac{2 π t}{3}) \Rightarrow y = 2

Maximum (3 n, 2)

Plug the extreme point

x = \frac{3}{2} + 3 n

into

2 cos (\frac{2 π t}{3}) \Rightarrow y = - 2

Minimum (\frac{3}{2} + 3 n, - 2)

Maximum (3 n, 2), Minimum (\frac{3}{2} + 3 n, - 2)

What is the extreme 2cos((2pit)/3) ?
The extreme 2cos((2pit)/3) is Maximum(3n,2),Minimum(3/2+3n,-2)