anonymous
  • anonymous
Can you help me find the critical points of this equation? h(x)=x^2lnx^2
OCW Scholar - Single Variable Calculus
chestercat
  • chestercat
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anonymous
  • anonymous
Yes.
anonymous
  • anonymous
i think h(x) has only one asymptote on x=0 and has 1 critical point at x=e^-1/2
anonymous
  • anonymous
actually, i think there are two critical points, one at x=e^1/2 and another at x=-e^1/2

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anonymous
  • anonymous
First solve for h'(x) \[h\prime(x)=x^{2}(\frac{ 2x }{ x^{2}})+2xln(x^{2})\] \[h \prime(x) =2x(1+\ln(x ^{2}))\] Equating h'(x)=0 will give you the first critical point, which is x=0. We can find the other two by equating 1+ln(x^2)=0 \[-1=\ln (x ^{2})\] \[e ^{-1}=x^2\] \[\frac{ 1 }{e }=x^2\] \[x= \pm \sqrt{\frac{ 1 }{ e }}\]

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