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

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

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

inflection points

f (x) = x^{2} \cdot ln (\frac{x}{2})

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

Solution steps

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

Find intervals:

Concave Downward

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

Concave Upward

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

Plug

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

into

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

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

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