What is the extreme f(x)=4cos(2x)-4,(0,2pi) ?

The extreme f(x)=4cos(2x)-4,(0,2pi) is Minimum(pi/2 ,-8),Maximum(pi,0),Minimum((3pi)/2 ,-8)

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extreme f(x)=4cos(2x)-4,(0,2pi)

extreme points

f (x) = 4 cos (2 x) - 4, (0, 2 π)

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

Solution steps

Find the critical points:

x = \frac{π}{2}, x = π, x = \frac{3 π}{2}

Domain of

4 cos (2 x) - 4, (0, 2 π) : 0 < x < 2 π

Find intervals:

Decreasing

: 0 < x < \frac{π}{2},

Increasing

: \frac{π}{2} < x < π,

Decreasing

: π < x < \frac{3 π}{2},

Increasing

: \frac{3 π}{2} < x < 2 π

Plug the extreme point

x = \frac{π}{2}

into

4 cos (2 x) - 4 \Rightarrow y = - 8

Minimum (\frac{π}{2}, - 8)

Plug the extreme point

x = π

into

4 cos (2 x) - 4 \Rightarrow y = 0

Maximum (π, 0)

Plug the extreme point

x = \frac{3 π}{2}

into

4 cos (2 x) - 4 \Rightarrow y = - 8

Minimum (\frac{3 π}{2}, - 8)

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

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432 y^{783}

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What is the extreme f(x)=4cos(2x)-4,(0,2pi) ?
The extreme f(x)=4cos(2x)-4,(0,2pi) is Minimum(pi/2 ,-8),Maximum(pi,0),Minimum((3pi)/2 ,-8)