What are the critical numbers of $f(x) = x^2*(1 + 3 ln x)$ ?

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Answer 1 · 2017-03-17T20:06:29

The only critical number is $x = e^(-5/6)$

$f'(x) = 2x(1+3lnx)+x^2(3/x)= x(6lnx+5)$

$f'(x)$ is defined for all $x$ in the domain of $f$ and

$f'(x)=0$ at $lnx = -5/6$ so $x = e^(-5/6)$ .

What are the critical numbers of f(x) = x^2*(1 + 3 ln x)f(x) = x^2*(1 + 3 ln x)?