What is the critical f(x)=csc(x) ?

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

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critical f(x)=csc(x)

critical points

f (x) = 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) = 9 (x - 4)^{\frac{2}{3}}

lo g_{2} (\frac{2 - 3 x}{3 - x})

- x^{2} + 7 x - 6

\frac{2 x ^{2}}{x ^{2} + 1}

\frac{5 t + 1}{t ^{3} - t ^{2} - 8 t}

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