What is the extreme f(x)=-6cos(x-2pi) ?

The extreme f(x)=-6cos(x-2pi) is Minimum(2pin,-6),Maximum(pi+2pin,6)

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extreme f(x)=-6cos(x-2pi)

extreme points

f (x) = - 6 cos (x - 2 π)

Minimum (2 πn, - 6), Maximum (π + 2 πn, 6)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

- 6 cos (x - 2 π) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

- 6 cos (x - 2 π) \Rightarrow y = - 6

Minimum (2 πn, - 6)

Plug the extreme point

x = π + 2 πn

into

- 6 cos (x - 2 π) \Rightarrow y = 6

Maximum (π + 2 πn, 6)

Minimum (2 πn, - 6), Maximum (π + 2 πn, 6)

What is the extreme f(x)=-6cos(x-2pi) ?
The extreme f(x)=-6cos(x-2pi) is Minimum(2pin,-6),Maximum(pi+2pin,6)