What is the extreme 5sin^2(x) ?

The extreme 5sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,5)

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extreme 5sin^2(x)

extreme points

5 sin^{2} (x)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 5)

Solution steps

Find the critical points:

x = πn, x = \frac{π}{2} + πn

Domain of

5 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

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

Minimum (πn, 0)

Plug the extreme point

x = \frac{π}{2} + πn

into

5 sin^{2} (x) \Rightarrow y = 5

Maximum (\frac{π}{2} + πn, 5)

Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 5)

f (x) = - x^{2} + 3 x + 5

f (x, y) = x^{3} y^{2} - 3 x y

f (x) = \frac{x ^{2} - 1}{4 - x ^{2}}

f (x, y) = - 2 x^{2} + 8 x - 3 y^{2} + 24 y + 7

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

What is the extreme 5sin^2(x) ?
The extreme 5sin^2(x) is Minimum(pin,0),Maximum(pi/2+pin,5)