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

The critical f(x)= 1/2 ln((1+x)/(1-x))-2x is x=-1/(sqrt(2)),x= 1/(sqrt(2))

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

critical points

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

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

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

\frac{1}{2} ln (\frac{1 + x}{1 - x}) - 2 x : - 1 < x < 1

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

is not defined at

x = - 1, x = 1

, therefore:

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

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

f (x) = 2 x^{2} + y^{2} + 4 x - 4 y + 5

f (x) = x^{8} ln (x)

f (x) = 2 x^{6} - 3 x^{4}

f (x) = \frac{1}{3} x^{3} - x^{2} - 3 x + 10

What is the critical f(x)= 1/2 ln((1+x)/(1-x))-2x ?
The critical f(x)= 1/2 ln((1+x)/(1-x))-2x is x=-1/(sqrt(2)),x= 1/(sqrt(2))