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

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

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

extreme points

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)

y = x^{3} - 6 x^{2} + 15

f (x) = (\frac{x ^{2} - 1}{( 5 - x ^{2} ) ^{0.5}})

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 1

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 8

y = x^{\frac{4}{7}} (x^{2} - 2)

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