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

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

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

extreme points

f (x) = 5 cos^{2} (x), 0 \leq x \leq π

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

Solution steps

Find the critical points:

x = 0, x = \frac{π}{2}, x = π

Domain of

5 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

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

Maximum (0, 5)

Plug the extreme point

x = \frac{π}{2}

into

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

Minimum (\frac{π}{2}, 0)

Plug the extreme point

x = π

into

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

Maximum (π, 5)

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

- 2 x^{2} - 12 x - 13

f (x) = - (x + 1) (x - 3)^{2}

y = x^{4} - 8 x^{2} + 3

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

f (x, y) = 2 x^{2} + 3 y^{2} + 2 x y + 14 x - 28 y

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