What is the inflection f(x)=(e^x)/(3+e^x) ?

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

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inflection f(x)=(e^x)/(3+e^x)

inflection points

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

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

Solution steps

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

Find intervals:

Concave Upward

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

Concave Downward

: ln (3) < x < \infty

Plug

x = ln (3)

into

\frac{e ^{x}}{3 + e ^{x}} : \frac{1}{2}

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

d o main \frac{x}{x ^{2} + 4}

in v erse (x - 1)^{3} + 2

a sy m pt o t es \frac{x ^{3} + x ^{2} - 6 x}{4 x ^{2} + 4 x - 8}

d o main f (x) = \frac{x - 4}{x ^{2} - 2 x - 8}

in t erce pt s x^{4} + 62 x^{2} + 128 x + 65

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