What is the inflection 5x^2ln(x/4) ?

The inflection 5x^2ln(x/4) is (4/(e^{3/2)},-(120)/(e^3))

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inflection 5x^2ln(x/4)

inflection points

5 x^{2} ln (\frac{x}{4})

(\frac{4}{e ^{\frac{3}{2}}}, - \frac{120}{e ^{3}})

Solution steps

f^{''} (x) = 5 (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

5 x^{2} ln (\frac{x}{4}) : - \frac{120}{e ^{3}}

(\frac{4}{e ^{\frac{3}{2}}}, - \frac{120}{e ^{3}})

8 y - 2 x = - 72

f (x) = \frac{1}{( x - 2 ) ^{2}}

(0.5) (2.1)

f (x) = 10 - \frac{5}{x}

f (x) = \frac{x + 4}{x - 3}

What is the inflection 5x^2ln(x/4) ?
The inflection 5x^2ln(x/4) is (4/(e^{3/2)},-(120)/(e^3))