What is the critical f(x)=((x-1)(x^2+4))/(x(x+1)) ?

The critical f(x)=((x-1)(x^2+4))/(x(x+1)) is x\approx-3.79804…,x\approx-0.39190…

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critical f(x)=((x-1)(x^2+4))/(x(x+1))

critical points

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

x \approx - 3.79804 \dots, x \approx - 0.39190 \dots

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x \approx - 3.79804 \dots, x \approx - 0.39190 \dots, x = - 1, x = 0

Identify critical points not in

f (x)

domain

Domain of

\frac{( x - 1 ) ( x ^{2} + 4 )}{x ( x + 1 )} : x < - 1 or - 1 < x < 0 or x > 0

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

is not defined at

x = - 1, x = 0

, therefore:

x \approx - 3.79804 \dots, x \approx - 0.39190 \dots

56 n^{2} + 9 n + 9

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

f (x) = 2 x^{2} + 4 x + 2

4 x^{3} - 12 x^{2}

f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

What is the critical f(x)=((x-1)(x^2+4))/(x(x+1)) ?
The critical f(x)=((x-1)(x^2+4))/(x(x+1)) is x\approx-3.79804…,x\approx-0.39190…