What is the inflection f(x)=(e^x)/(8+e^x) ?

The inflection f(x)=(e^x)/(8+e^x) is (3ln(2), 1/2)

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inflection f(x)=(e^x)/(8+e^x)

inflection points

f (x) = \frac{e ^{x}}{8 + e ^{x}}

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

Solution steps

f^{''} (x) = \frac{8 e ^{x} ( - e ^{x} + 8 )}{( 8 + e ^{x} ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < 3 ln (2),

Concave Downward

: 3 ln (2) < x < \infty

Plug

x = 3 ln (2)

into

\frac{e ^{x}}{8 + e ^{x}} : \frac{1}{2}

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

f (x) = - 10

(\frac{1}{8}, - \frac{4}{9}), (- \frac{5}{2}, \frac{5}{2})

f (x) = 2 x^{2} - 6 x + 8

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

y = \frac{1}{3} x - 2

What is the inflection f(x)=(e^x)/(8+e^x) ?
The inflection f(x)=(e^x)/(8+e^x) is (3ln(2), 1/2)