What is the critical (1-x)/(2sqrt(x)(1+x)^2) ?

The critical (1-x)/(2sqrt(x)(1+x)^2) is x=(3+2sqrt(3))/3

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critical (1-x)/(2sqrt(x)(1+x)^2)

critical points

\frac{1 - x}{2 x ( 1 + x ) ^{2}}

x = \frac{3 + 2 3}{3}

Solution steps

\frac{1 - x}{2 x ( 1 + x ) ^{2}}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{3 + 2 3}{3}, x = 0

Identify critical points not in

f (x)

domain

Domain of

\frac{1 - x}{2 x ( 1 + x ) ^{2}} : x > 0

\frac{1 - x}{2 x ( 1 + x ) ^{2}}

is not defined at

x = 0

, therefore:

x = \frac{3 + 2 3}{3}

f (x) = x^{3} - 2 x^{2} - 35 x

f (x) = 4

\frac{x}{x ^{2} + 3 x + 2}

\frac{4}{x ^{3}}

f (x) = x^{2} - 12 x + 9

What is the critical (1-x)/(2sqrt(x)(1+x)^2) ?
The critical (1-x)/(2sqrt(x)(1+x)^2) is x=(3+2sqrt(3))/3