What is the inflection (x+x)/((1+2ln(2x))) ?

The inflection (x+x)/((1+2ln(2x))) is ((e^{3/2})/2 ,(e^{3/2})/4)

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inflection (x+x)/((1+2ln(2x)))

inflection points

\frac{x + x}{( 1 + 2 ln ( 2 x ) )}

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

Solution steps

f^{''} (x) = \frac{4 ( - 2 ln ( 2 x ) + 3 )}{x ( 2 ln ( 2 x ) + 1 ) ^{3}}

Find intervals:

Concave Downward

: 0 < x < \frac{1}{2 e},

Concave Upward

: \frac{1}{2 e} < x < \frac{e ^{\frac{3}{2}}}{2},

Concave Downward

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

Plug

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

into

\frac{x + x}{1 + 2 ln ( 2 x )} : \frac{e ^{\frac{3}{2}}}{4}

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

What is the inflection (x+x)/((1+2ln(2x))) ?
The inflection (x+x)/((1+2ln(2x))) is ((e^{3/2})/2 ,(e^{3/2})/4)