What is the critical f(x)=xln(2x) ?

The critical f(x)=xln(2x) is x= 1/(2e)

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critical f(x)=xln(2x)

critical points

f (x) = x ln (2 x)

x = \frac{1}{2 e}

Solution steps

x ln (2 x)

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{1}{2 e}, x = 0

Identify critical points not in

f (x)

domain

Domain of

x ln (2 x) : x > 0

x ln (2 x)

is not defined at

x = 0

, therefore:

x = \frac{1}{2 e}

f (x) = ln (x^{2} - 4)

f (x) = 2 x^{3} - 15 x^{2} + 36 x

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

f (x) = cos (x) + sin (x)

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