What is the extreme f(x)=-3csc(x) ?

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

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extreme f(x)=-3csc(x)

extreme points

f (x) = - 3 csc (x)

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

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Domain of

- 3 csc (x) : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Find intervals:

Increasing

: 2 πn < x < \frac{π}{2} + 2 πn,

Decreasing

: \frac{π}{2} + 2 πn < x < π + 2 πn,

Decreasing

: π + 2 πn < x < \frac{3 π}{2} + 2 πn,

Increasing

: \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

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

Maximum (\frac{π}{2} + 2 πn, - 3)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

- 3 csc (x) \Rightarrow y = 3

Minimum (\frac{3 π}{2} + 2 πn, 3)

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

f (x) = \frac{x ^{3}}{3} - 375 x^{2} + 129600 x

f (x) = e^{4 x - x^{2}}

f (x, y) = x^{2} + 4 y^{2} - 6 x + 8 y + 2

f (x, y) = x^{2} - y^{2} + 9

(x + 3)^{2} + 1

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