What are the critical values, if any, of $f (x) = x^{6} ln (x)$ $f(x)= x^6ln(x)$ ?

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Answer 1 · 2018-07-04T16:15:43

$x = 0$ $x=0$ or $x = e^{- \frac{1}{6}}$ $x=e^(-1/6)$

$(uv)'=u'v+uv'$
and the fact that

$(ln(x))'=1/x$

so we get

$f'(x)=6x^5+x^6*1/x$

$f'(x)=x^5(6ln(x)+1)$
solving $f'(x)=0$
we get

$x=0$ or $x=e^(-1/6)$

What are the critical values, if any, of f(x)= x^6ln(x) f(x)=x6ln(x)f(x)= x^6ln(x) ?