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

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

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

extreme points

f (x) = 2 - 4 (sin^{2} (x))

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)

f (x) = 4 x y - x^{4} - 2 y^{2}

f (x) = \frac{x ^{2} ( x - 3 )}{x + 6}

f (x) = f (x) = x x^{2} + 4

f (x) = 2 x^{3} + 3 x^{2} - 120 x + 9

f (x) = x^{3} + 12 x^{2} - 27 x + 6, - 10 \leq x \leq 0

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