What is the extreme g(x)=8-5sin(x),0<= x<= pi ?

The extreme g(x)=8-5sin(x),0<= x<= pi is Maximum(0,8),Minimum(pi/2 ,3),Maximum(pi,8)

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extreme g(x)=8-5sin(x),0<= x<= pi

extreme points

g (x) = 8 - 5 sin (x), 0 \leq x \leq π

Maximum (0, 8), Minimum (\frac{π}{2}, 3), Maximum (π, 8)

Solution steps

Find the critical points:

x = 0, x = \frac{π}{2}, x = π

Domain of

8 - 5 sin (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

8 - 5 sin (x) \Rightarrow y = 8

Maximum (0, 8)

Plug the extreme point

x = \frac{π}{2}

into

8 - 5 sin (x) \Rightarrow y = 3

Minimum (\frac{π}{2}, 3)

Plug the extreme point

x = π

into

8 - 5 sin (x) \Rightarrow y = 8

Maximum (π, 8)

Maximum (0, 8), Minimum (\frac{π}{2}, 3), Maximum (π, 8)

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

f (x) = 13 x + \frac{1}{x}

f (x) = - 3 t^{2} + 132 t + 100

f (x) = 3 x

3 x^{2} - 12 x + 2 y^{2} - 8 y + 7

What is the extreme g(x)=8-5sin(x),0<= x<= pi ?
The extreme g(x)=8-5sin(x),0<= x<= pi is Maximum(0,8),Minimum(pi/2 ,3),Maximum(pi,8)