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

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

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

critical points

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

x = - \frac{1}{2}

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{1}{2}, x = - 1, x = 0

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 1, x = 0

, therefore:

x = - \frac{1}{2}

3 x^{3} + x y^{2} - 2 x y + 1

f (x) = 4 x^{3} - 9 x^{2} + 3 x + 1

3 x^{2} - 12 x

f (x) = x^{3} + 3 x^{2} - 45 x + 8

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