What is the inflection f(x)=(e^x)/(4+e^x) ?

The inflection f(x)=(e^x)/(4+e^x) is (2ln(2), 1/2)

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inflection f(x)=(e^x)/(4+e^x)

inflection points

f (x) = \frac{e ^{x}}{4 + e ^{x}}

(2 ln (2), \frac{1}{2})

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < 2 ln (2),

Concave Downward

: 2 ln (2) < x < \infty

Plug

x = 2 ln (2)

into

\frac{e ^{x}}{4 + e ^{x}} : \frac{1}{2}

(2 ln (2), \frac{1}{2})

What is the inflection f(x)=(e^x)/(4+e^x) ?
The inflection f(x)=(e^x)/(4+e^x) is (2ln(2), 1/2)