What is the extreme f(x)=3cos(x),0<= x<= 2pi ?

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

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extreme f(x)=3cos(x),0<= x<= 2pi

extreme points

f (x) = 3 cos (x), 0 \leq x \leq 2 π

Maximum (0, 3), Minimum (π, - 3), Maximum (2 π, 3)

Solution steps

Find the critical points:

x = 0, x = π, x = 2 π

Domain of

3 cos (x), 0 \leq x \leq 2 π : 0 \leq x \leq 2 π

Find intervals:

Decreasing

: 0 < x < π,

Increasing

: π < x < 2 π

Plug the extreme point

x = 0

into

3 cos (x) \Rightarrow y = 3

Maximum (0, 3)

Plug the extreme point

x = π

into

3 cos (x) \Rightarrow y = - 3

Minimum (π, - 3)

Plug the extreme point

x = 2 π

into

3 cos (x) \Rightarrow y = 3

Maximum (2 π, 3)

Maximum (0, 3), Minimum (π, - 3), Maximum (2 π, 3)

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