What is the inflection y=x^2*ln(x/8) ?

The inflection y=x^2*ln(x/8) is (8/(e^{3/2)},-(96)/(e^3))

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inflection y=x^2*ln(x/8)

inflection

(\frac{8}{e ^{\frac{3}{2}}}, - \frac{96}{e ^{3}})

Solution steps

f^{''} (x) = 2 ln (\frac{x}{8}) + 3

Find intervals:

Concave Downward

: 0 < x < \frac{8}{e ^{\frac{3}{2}}},

Concave Upward

: \frac{8}{e ^{\frac{3}{2}}} < x < \infty

Plug

x = \frac{8}{e ^{\frac{3}{2}}}

into

x^{2} \cdot ln (\frac{x}{8}) : - \frac{96}{e ^{3}}

(\frac{8}{e ^{\frac{3}{2}}}, - \frac{96}{e ^{3}})

What is the inflection y=x^2*ln(x/8) ?
The inflection y=x^2*ln(x/8) is (8/(e^{3/2)},-(96)/(e^3))