What is the extreme f(x)=4sin^2(x),0<= x<= pi ?

The extreme f(x)=4sin^2(x),0<= x<= pi is Minimum(0,0),Maximum(pi/2 ,4),Minimum(pi,0)

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extreme f(x)=4sin^2(x),0<= x<= pi

extreme points

f (x) = 4 sin^{2} (x), 0 \leq x \leq π

Minimum (0, 0), Maximum (\frac{π}{2}, 4), Minimum (π, 0)

Solution steps

Find the critical points:

x = 0, x = \frac{π}{2}, x = π

Domain of

4 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

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

Minimum (0, 0)

Plug the extreme point

x = \frac{π}{2}

into

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

Maximum (\frac{π}{2}, 4)

Plug the extreme point

x = π

into

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

Minimum (π, 0)

Minimum (0, 0), Maximum (\frac{π}{2}, 4), Minimum (π, 0)

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

f (x, y) = 4 x^{2} + \frac{1}{4} y^{3} - 2 x y

f (x) = 8 x + 7 x^{- 1}

f (x) = x^{3} + 6 x^{2} + 12 x + 7

f (p, q) = 3 p^{3} + 4 q^{3} - 2 p^{2} q - 4 p - 5 q

What is the extreme f(x)=4sin^2(x),0<= x<= pi ?
The extreme f(x)=4sin^2(x),0<= x<= pi is Minimum(0,0),Maximum(pi/2 ,4),Minimum(pi,0)