What is the extreme f(x)=-5cos(x-3pi) ?

The extreme f(x)=-5cos(x-3pi) is Maximum(2pin,5),Minimum(pi+2pin,-5)

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extreme f(x)=-5cos(x-3pi)

extreme points

f (x) = - 5 cos (x - 3 π)

Maximum (2 πn, 5), Minimum (π + 2 πn, - 5)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

- 5 cos (x - 3 π) : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn < x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

- 5 cos (x - 3 π) \Rightarrow y = 5

Maximum (2 πn, 5)

Plug the extreme point

x = π + 2 πn

into

- 5 cos (x - 3 π) \Rightarrow y = - 5

Minimum (π + 2 πn, - 5)

Maximum (2 πn, 5), Minimum (π + 2 πn, - 5)

What is the extreme f(x)=-5cos(x-3pi) ?
The extreme f(x)=-5cos(x-3pi) is Maximum(2pin,5),Minimum(pi+2pin,-5)