What is the critical f(x)=x-5x^{1/3} ?

The critical f(x)=x-5x^{1/3} is x=-(5sqrt(5))/(3sqrt(3)),x=0,x=(5sqrt(5))/(3sqrt(3))

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critical f(x)=x-5x^{1/3}

critical points

f (x) = x - 5 x^{\frac{1}{3}}

x = - \frac{5 5}{3 3}, x = 0, x = \frac{5 5}{3 3}

Solution steps

x - 5 x^{\frac{1}{3}}

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{5 5}{3 3}, x = \frac{5 5}{3 3}, x = 0

Identify critical points not in

f (x)

domain

Domain of

x - 5 x^{\frac{1}{3}} : - \infty < x < \infty

All critical points are in domain

x = - \frac{5 5}{3 3}, x = 0, x = \frac{5 5}{3 3}

\frac{2 x ^{2} + 2 x - 4}{x ^{2} + x}

f (x) = 1 - e^{- x}

x^{2} e^{x}

4 - 9 x

6 x + 7 y = 3, (9, 0)

What is the critical f(x)=x-5x^{1/3} ?
The critical f(x)=x-5x^{1/3} is x=-(5sqrt(5))/(3sqrt(3)),x=0,x=(5sqrt(5))/(3sqrt(3))