What is the critical csc(x) ?

The critical csc(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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critical csc(x)

critical points

csc (x)

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

Solution steps

csc (x)

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

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

csc (x)

is not defined at

x = 2 πn, x = π + 2 πn

, therefore:

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

f (x) = 16 - x^{2}

13, - 11

f (x) = 3 x^{2} - 2

(3.2) (7.6)

f (x) = - 4 cos (x + \frac{π}{4})

What is the critical csc(x) ?
The critical csc(x) is x= pi/2+2pin,x=(3pi)/2+2pin