What is the critical f(x)=xln(3x) ?

The critical f(x)=xln(3x) is x= 1/(3e)

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critical f(x)=xln(3x)

critical points

f (x) = x ln (3 x)

x = \frac{1}{3 e}

Solution steps

x ln (3 x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{1}{3 e}, x = 0

Identify critical points not in

f (x)

domain

Domain of

x ln (3 x) : x > 0

x ln (3 x)

is not defined at

x = 0

, therefore:

x = \frac{1}{3 e}

\frac{x ^{3} - 16 x}{- 3 x ^{2} + 3 x + 18}

f (x) = x^{4} + 8 x^{2} + 16

f (x) = - e^{x + 7}

(- 3, - 5), (- 0.5, 0)

\frac{( x ^{2} - 5 )}{7 x ^{2}}