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

The critical f(x)=-(2(x^2-1))/(x^2-4) is x=0

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

critical points

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

x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 2, x = 2

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 2, x = 2

, therefore:

x = 0

f (x, y) = x e^{- 2 x^{2} - 2 y^{2}}

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

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

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

f (x) = x^{3} - 9 x^{2} + 24 x - 7

What is the critical f(x)=-(2(x^2-1))/(x^2-4) ?
The critical f(x)=-(2(x^2-1))/(x^2-4) is x=0