What is the extreme 5sin^2(x),0<= x<= pi ?

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

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extreme 5sin^2(x),0<= x<= pi

extreme points

5 sin^{2} (x), 0 \leq x \leq π

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

Solution steps

Find the critical points:

x = 0, x = \frac{π}{2}, x = π

Domain of

5 sin^{2} (x), 0 \leq x \leq π : 0 \leq x \leq π

Find intervals:

Increasing

: 0 < x < \frac{π}{2},

Decreasing

: \frac{π}{2} < x < π

Plug the extreme point

x = 0

into

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

Minimum (0, 0)

Plug the extreme point

x = \frac{π}{2}

into

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

Maximum (\frac{π}{2}, 5)

Plug the extreme point

x = π

into

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

Minimum (π, 0)

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

f (x) = - x^{3} + 3 x - 11

f (x) = 2 x^{3} - 3 x^{2} - 4

f (x) = - 12 x^{3} + 2 x^{2} - 3

f (x) = x^{3} - 2 x^{2} - 15 x + 10 [- 2]

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

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