What is the critical f(x)=(4x)/(3(x^2-4)^{1/3)} ?

The critical f(x)=(4x)/(3(x^2-4)^{1/3)} is x=-2sqrt(3),x=2sqrt(3)

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critical f(x)=(4x)/(3(x^2-4)^{1/3)}

critical points

f (x) = \frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

x = - 23, x = 23

Solution steps

\frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

Find where

f^{'} (x)

is equal to zero or undefined

x = - 23, x = 23, x = - 2, x = 2

Identify critical points not in

f (x)

domain

Domain of

\frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}} : x < - 2 or - 2 < x < 2 or x > 2

\frac{4 x}{3 ( x ^{2} - 4 ) ^{\frac{1}{3}}}

is not defined at

x = - 2, x = 2

, therefore:

x = - 23, x = 23

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

f (x) = x + \frac{36}{x}

f (x) = 9 x^{4} + 6 x^{3} + 1

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

f (x) = - 4 sin (2 x)

What is the critical f(x)=(4x)/(3(x^2-4)^{1/3)} ?
The critical f(x)=(4x)/(3(x^2-4)^{1/3)} is x=-2sqrt(3),x=2sqrt(3)