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

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

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

extreme

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

Increasing

: 0 < x < π,

Decreasing

: π < x < 2 π

Plug the extreme point

x = 0

into

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

Minimum (0, - 3)

Plug the extreme point

x = π

into

- 3 cos (x) \Rightarrow y = 3

Maximum (π, 3)

Plug the extreme point

x = 2 π

into

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

Minimum (2 π, - 3)

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

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