What is the extreme sin^2(x) ?

The extreme sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,1)

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extreme sin^2(x)

extreme points

sin^{2} (x)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 1)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

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

Find intervals:

Increasing

: πn < x < \frac{π}{2} + πn,

Decreasing

: \frac{π}{2} + πn < x < π + πn

Plug the extreme point

x = πn

into

sin^{2} (x) \Rightarrow y = 0

Minimum (πn, 0)

Plug the extreme point

x = \frac{π}{2} + πn

into

sin^{2} (x) \Rightarrow y = 1

Maximum (\frac{π}{2} + πn, 1)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 1)

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

y = 3 sin (\frac{x}{2} \frac{- π}{3})

f (x) = (x - 3) (x + 2)

y = - (x + 3)^{2} - 1

- 2 y - 5 x = 2 - 10 x

What is the extreme sin^2(x) ?
The extreme sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,1)