What is the critical f(x)=((x-1)^{1/5})/(x+1) ?

The critical f(x)=((x-1)^{1/5})/(x+1) is x=1,x= 3/2

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critical f(x)=((x-1)^{1/5})/(x+1)

critical points

f (x) = \frac{( x - 1 ) ^{\frac{1}{5}}}{x + 1}

x = 1, x = \frac{3}{2}

Solution steps

\frac{( x - 1 ) ^{\frac{1}{5}}}{x + 1}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{3}{2}, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{( x - 1 ) ^{\frac{1}{5}}}{x + 1} : x < - 1 or x > - 1

\frac{( x - 1 ) ^{\frac{1}{5}}}{x + 1}

is not defined at

x = - 1

, therefore:

x = 1, x = \frac{3}{2}

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

y = \frac{- 2 ( x ^{2} - 1 )}{x ^{2} - 4}

f (x) = x^{5 x}

f (x) = 2 x^{3} + x^{2} - 20 x + 5

(12 - 6 x) e^{x}

What is the critical f(x)=((x-1)^{1/5})/(x+1) ?
The critical f(x)=((x-1)^{1/5})/(x+1) is x=1,x= 3/2