What is the critical y=(ln(x))/(x^2) ?

The critical y=(ln(x))/(x^2) is x=sqrt(e)

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critical y=(ln(x))/(x^2)

critical points

y = \frac{ln ( x )}{x ^{2}}

x = e

Solution steps

\frac{ln ( x )}{x ^{2}}

Find where

f^{'} (x)

is equal to zero or undefined

x = e, x = 0

Identify critical points not in

f (x)

domain

Domain of

\frac{ln ( x )}{x ^{2}} : x > 0

\frac{ln ( x )}{x ^{2}}

is not defined at

x = 0

, therefore:

x = e

f (x) = x^{3} - 6 x y + 8 y^{3}

f (x) = 3 x

f (x, y) = x^{3} - 6 x y + 8 y^{3}

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

f (x) = x e^{x^{2}}

What is the critical y=(ln(x))/(x^2) ?
The critical y=(ln(x))/(x^2) is x=sqrt(e)