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

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

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

extreme points

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) = x + \frac{9}{x} + 2, 1 \leq x \leq 18

f (x) = 7 x^{4} - 6 x^{2} - 1

x^{2} - 2 x y + y^{3} - y

f (x) = 4 x + \frac{4}{x}

f (x) = 7 x^{4} - 6 x^{2} - 6

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