What is the extreme f(x)=3cos(3x),-pi/2 <= x<= pi/2 ?

The extreme f(x)=3cos(3x),-pi/2 <= x<= pi/2 is

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extreme f(x)=3cos(3x),-pi/2 <= x<= pi/2

extreme points

f (x) = 3 cos (3 x), - \frac{π}{2} \leq x \leq \frac{π}{2}

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

Solution steps

Find the critical points:

x = - \frac{π}{2}, x = - \frac{π}{3}, x = 0, x = \frac{π}{3}, x = \frac{π}{2}

Domain of

3 cos (3 x), - \frac{π}{2} \leq x \leq \frac{π}{2} : - \frac{π}{2} \leq x \leq \frac{π}{2}

Find intervals:

Decreasing

: - \frac{π}{2} < x < - \frac{π}{3},

Increasing

: - \frac{π}{3} < x < 0,

Decreasing

: 0 < x < \frac{π}{3},

Increasing

: \frac{π}{3} < x < \frac{π}{2}

Plug the extreme point

x = - \frac{π}{2}

into

3 cos (3 x) \Rightarrow y = 0

Maximum (- \frac{π}{2}, 0)

Plug the extreme point

x = - \frac{π}{3}

into

3 cos (3 x) \Rightarrow y = - 3

Minimum (- \frac{π}{3}, - 3)

Plug the extreme point

x = 0

into

3 cos (3 x) \Rightarrow y = 3

Maximum (0, 3)

Plug the extreme point

x = \frac{π}{3}

into

3 cos (3 x) \Rightarrow y = - 3

Minimum (\frac{π}{3}, - 3)

Plug the extreme point

x = \frac{π}{2}

into

3 cos (3 x) \Rightarrow y = 0

Maximum (\frac{π}{2}, 0)

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

What is the extreme f(x)=3cos(3x),-pi/2 <= x<= pi/2 ?
The extreme f(x)=3cos(3x),-pi/2 <= x<= pi/2 is