What is the critical x/(3x-4ln(x)) ?

The critical x/(3x-4ln(x)) is x=e

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critical x/(3x-4ln(x))

critical points

\frac{x}{3 x - 4 ln ( x )}

x = e

Solution steps

\frac{x}{3 x - 4 ln ( x )}

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{x}{3 x - 4 ln ( x )} : x > 0

\frac{x}{3 x - 4 ln ( x )}

is not defined at

x = 0

, therefore:

x = e

f (x) = 5 x^{4} - 3 x^{3} + 3 x^{2} - 5 x + 7

f (x, y) = 2 x^{3} + y^{3} + 3 x^{2} - 3 y - 12 x - 4

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

f (x, y) = 4 x y - y^{4} - 2 x^{2}

x^{4} + x^{2} - 6 x y + 3 y^{2}