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

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

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critical f(x)= x/(1-x)-(x^2)/(1+x)

critical points

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

x = - 2 + 5, x = 2 + 5

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = - 2 + 5, x = 2 + 5, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

\frac{x}{1 - x} - \frac{x ^{2}}{1 + x} : x < - 1 or - 1 < x < 1 or x > 1

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

is not defined at

x = - 1, x = 1

, therefore:

x = - 2 + 5, x = 2 + 5

\frac{1}{x}

{x^{2} : x < - 2, ln (x + 5) : x \geq - 2}

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

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

x^{4} - 7 x^{3}

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