What is the inflection f(x)=3x^2ln(x/4) ?

The inflection f(x)=3x^2ln(x/4) is (4/(e^{3/2)},-(72)/(e^3))

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inflection f(x)=3x^2ln(x/4)

inflection points

f (x) = 3 x^{2} ln (\frac{x}{4})

(\frac{4}{e ^{\frac{3}{2}}}, - \frac{72}{e ^{3}})

Solution steps

f^{''} (x) = 3 (2 ln (\frac{x}{4}) + 3)

Find intervals:

Concave Downward

: 0 < x < \frac{4}{e ^{\frac{3}{2}}},

Concave Upward

: \frac{4}{e ^{\frac{3}{2}}} < x < \infty

Plug

x = \frac{4}{e ^{\frac{3}{2}}}

into

3 x^{2} ln (\frac{x}{4}) : - \frac{72}{e ^{3}}

(\frac{4}{e ^{\frac{3}{2}}}, - \frac{72}{e ^{3}})

What is the inflection f(x)=3x^2ln(x/4) ?
The inflection f(x)=3x^2ln(x/4) is (4/(e^{3/2)},-(72)/(e^3))