What is the extreme cos(2φ) ?

The extreme cos(2φ) is Maximum(pin,1),Minimum(pi/2+pin,-1)

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extreme cos(2φ)

extreme points

cos (2 φ)

Maximum (πn, 1), Minimum (\frac{π}{2} + πn, - 1)

Solution steps

Find the critical points:

φ = πn, φ = \frac{π}{2} + πn

Domain of

cos (2 φ) : - \infty < φ < \infty

Find intervals:

Decreasing

: πn < φ < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < φ < π + πn

Plug the extreme point

x = πn

into

cos (2 φ) \Rightarrow y = 1

Maximum (πn, 1)

Plug the extreme point

x = \frac{π}{2} + πn

into

cos (2 φ) \Rightarrow y = - 1

Minimum (\frac{π}{2} + πn, - 1)

Maximum (πn, 1), Minimum (\frac{π}{2} + πn, - 1)

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