Point of inflexion, help plz (1 Viewer)

excellence1 · Feb 20, 2016

Find the Point of inflexion on the curve y= xlnx - x^2

InteGrand · Feb 20, 2016

excellence1 said:
Find the Point of inflexion on the curve y= xlnx - x^2

$\noindent Let $f(x) = x \ln x -x^2$, $x>0$. Then $f^\prime (x) = \ln x + 1 -2x$ and $f'' (x) = \frac{1}{x} -2$. So $f''(x) =0$ if and only if $x=\frac{1}{2}$, and it is clear that $f'' (x)$ indeed changes sign here. So the inflection point is at $x =\frac{1}{2}$. At this point, $y = -\frac{1}{2} \ln 2 -\frac{1}{4}$. So the inflection point is $\left(\frac{1}{2}, -\frac{1}{2}\ln 2 -\frac{1}{4}\right)$.$

Point of inflexion, help plz (1 Viewer)

excellence1

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InteGrand

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