What is the critical y=-2csc(3x+pi)-1 ?

The critical y=-2csc(3x+pi)-1 is x= pi/6+(2pi)/3 n,x= pi/2+(2pi)/3 n

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critical y=-2csc(3x+pi)-1

critical points

y = - 2 csc (3 x + π) - 1

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

Solution steps

- 2 csc (3 x + π) - 1

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{2 π}{3} n, x = \frac{π}{3} + \frac{2 π}{3} n

Identify critical points not in

f (x)

domain

Domain of

- 2 csc (3 x + π) - 1 : \frac{2 π}{3} n < x < \frac{π}{3} + \frac{2 π}{3} n or \frac{π}{3} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

- 2 csc (3 x + π) - 1

is not defined at

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

, therefore:

x = \frac{π}{6} + \frac{2 π}{3} n, x = \frac{π}{2} + \frac{2 π}{3} n

f (x) = 6 x^{5} + 33 x^{4} + 30 x^{3} + 100

f (x) = x^{4} (3 x - 1)^{6}

f (x) = x^{3} - 12 x y^{2} + 48 y^{2}

x^{2} e^{16 x}

2 e^{- x} x - e^{- x} x^{2}

What is the critical y=-2csc(3x+pi)-1 ?
The critical y=-2csc(3x+pi)-1 is x= pi/6+(2pi)/3 n,x= pi/2+(2pi)/3 n