What is the extreme f(x)=2-4(sin(x))^2 ?

The extreme f(x)=2-4(sin(x))^2 is Maximum(pin,2),Minimum(pi/2+pin,-2)

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extreme f(x)=2-4(sin(x))^2

extreme

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

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

2 - 4 sin^{2} (x) : - \infty < x < \infty

Find intervals:

Decreasing

: πn < x < \frac{π}{2} + πn,

Increasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

2 - 4 sin^{2} (x) \Rightarrow y = 2

Maximum (πn, 2)

Plug the extreme point

x = \frac{π}{2} + πn

into

2 - 4 sin^{2} (x) \Rightarrow y = - 2

Minimum (\frac{π}{2} + πn, - 2)

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

What is the extreme f(x)=2-4(sin(x))^2 ?
The extreme f(x)=2-4(sin(x))^2 is Maximum(pin,2),Minimum(pi/2+pin,-2)