What is the inflection f(x)=x^2ln(x/6) ?

The inflection f(x)=x^2ln(x/6) is (6/(e^{3/2)},-(54)/(e^3))

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inflection f(x)=x^2ln(x/6)

inflection

(\frac{6}{e ^{\frac{3}{2}}}, - \frac{54}{e ^{3}})

Solution steps

f^{''} (x) = 2 ln (\frac{x}{6}) + 3

Find intervals:

Concave Downward

: 0 < x < \frac{6}{e ^{\frac{3}{2}}},

Concave Upward

: \frac{6}{e ^{\frac{3}{2}}} < x < \infty

Plug

x = \frac{6}{e ^{\frac{3}{2}}}

into

x^{2} ln (\frac{x}{6}) : - \frac{54}{e ^{3}}

(\frac{6}{e ^{\frac{3}{2}}}, - \frac{54}{e ^{3}})

What is the inflection f(x)=x^2ln(x/6) ?
The inflection f(x)=x^2ln(x/6) is (6/(e^{3/2)},-(54)/(e^3))