What is the extreme f(x)=3cos^2(x),0<= x<= pi ?

The extreme f(x)=3cos^2(x),0<= x<= pi is Maximum(0,3),Minimum(pi/2 ,0),Maximum(pi,3)

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extreme f(x)=3cos^2(x),0<= x<= pi

extreme points

f (x) = 3 cos^{2} (x), 0 \leq x \leq π

Maximum (0, 3), Minimum (\frac{π}{2}, 0), Maximum (π, 3)

Solution steps

Find the critical points:

x = 0, x = \frac{π}{2}, x = π

Domain of

3 cos^{2} (x), 0 \leq x \leq π : 0 \leq x \leq π

Find intervals:

Decreasing

: 0 < x < \frac{π}{2},

Increasing

: \frac{π}{2} < x < π

Plug the extreme point

x = 0

into

3 cos^{2} (x) \Rightarrow y = 3

Maximum (0, 3)

Plug the extreme point

x = \frac{π}{2}

into

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

Minimum (\frac{π}{2}, 0)

Plug the extreme point

x = π

into

3 cos^{2} (x) \Rightarrow y = 3

Maximum (π, 3)

Maximum (0, 3), Minimum (\frac{π}{2}, 0), Maximum (π, 3)

f (x) = - 8 x^{\frac{6}{5}} + 4 x^{\frac{2}{5}}

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

f (x) = 4 - (x - 5)^{5}

f (x) = - 3 x x + 1

f (x) = - 20 x^{6} - 5 x^{3} + x^{2} - 17

What is the extreme f(x)=3cos^2(x),0<= x<= pi ?
The extreme f(x)=3cos^2(x),0<= x<= pi is Maximum(0,3),Minimum(pi/2 ,0),Maximum(pi,3)