What is the inflection f(x)=(e^x)/(5+e^x) ?

The inflection f(x)=(e^x)/(5+e^x) is (ln(5), 1/2)

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inflection f(x)=(e^x)/(5+e^x)

inflection points

f (x) = \frac{e ^{x}}{5 + e ^{x}}

(ln (5), \frac{1}{2})

Solution steps

f^{''} (x) = \frac{5 e ^{x} ( - e ^{x} + 5 )}{( 5 + e ^{x} ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < ln (5),

Concave Downward

: ln (5) < x < \infty

Plug

x = ln (5)

into

\frac{e ^{x}}{5 + e ^{x}} : \frac{1}{2}

(ln (5), \frac{1}{2})

f (x) = \frac{x + 2}{x ^{2} - 4}

f (x) = \frac{4 + x}{x + 5}

f (x) = e^{- x^{2}}

f (x) = \frac{x ^{2}}{x - 6}

x^{2} - 8 x + 12

What is the inflection f(x)=(e^x)/(5+e^x) ?
The inflection f(x)=(e^x)/(5+e^x) is (ln(5), 1/2)