What is the critical f(x)=x^{1/5}-x^{-4/5} ?

The critical f(x)=x^{1/5}-x^{-4/5} is x=-4

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critical f(x)=x^{1/5}-x^{-4/5}

critical points

f (x) = x^{\frac{1}{5}} - x^{- \frac{4}{5}}

x = - 4

Solution steps

x^{\frac{1}{5}} - x^{- \frac{4}{5}}

Find where

f^{'} (x)

is equal to zero or undefined

x = - 4, x = 0

Identify critical points not in

f (x)

domain

Domain of

x^{\frac{1}{5}} - x^{- \frac{4}{5}} : x < 0 or x > 0

x^{\frac{1}{5}} - x^{- \frac{4}{5}}

is not defined at

x = 0

, therefore:

x = - 4

f (x) = x^{\frac{4}{5}} (x - 5)^{2}

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

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

x^{2} + 4 x + 4

f (x) = \frac{x}{x ^{2} - 9}

What is the critical f(x)=x^{1/5}-x^{-4/5} ?
The critical f(x)=x^{1/5}-x^{-4/5} is x=-4