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

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

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

critical points

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

x = 0

Solution steps

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

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = - 1, x = 1

Identify critical points not in

f (x)

domain

Domain of

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

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

is not defined at

x = - 1, x = 1

, therefore:

x = 0

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

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

f (x) = 2 cos (4 x)

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

ψ (x) = x^{2} + 3 x, - 2 \leq x \leq 1

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