Question

Can you help me find the critical points of this equation? h(x)=x^2lnx^2

Answer 1

Yes.

Answer 2

i think h(x) has only one asymptote on x=0 and has 1 critical point at x=e^-1/2

Answer 3

actually, i think there are two critical points, one at x=e^1/2 and another at x=-e^1/2

Answer 4

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

\[-1=\ln (x ^{2})\]
\[e ^{-1}=x^2\]

\[\frac{ 1 }{e }=x^2\]

\[x= \pm \sqrt{\frac{ 1 }{ e }}\]