What is the critical f(x)=x^2*ln(x) ?

The critical f(x)=x^2*ln(x) is x= 1/(sqrt(e))

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critical f(x)=x^2*ln(x)

critical points

f (x) = x^{2} \cdot ln (x)

x = \frac{1}{e}

Solution steps

x^{2} ln (x)

Find where

f^{'} (x)

is equal to zero or undefined

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

Identify critical points not in

f (x)

domain

Domain of

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

x^{2} \cdot ln (x)

is not defined at

x = 0

, therefore:

x = \frac{1}{e}

f (x) = x^{3} + y^{3} + 3 x^{2} - 3 y^{2} - 8

x^{3} + 6 x^{2} - 15 x

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}

y = \frac{x ^{2}}{x ^{2} + 3}

f (x) = 2 x^{3} - 6 x^{2} - 18 x + 2

What is the critical f(x)=x^2*ln(x) ?
The critical f(x)=x^2*ln(x) is x= 1/(sqrt(e))