What is the inflection f(x)=(e^x)/(6+e^x) ?

The inflection f(x)=(e^x)/(6+e^x) is (ln(6), 1/2)

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inflection f(x)=(e^x)/(6+e^x)

inflection points

f (x) = \frac{e ^{x}}{6 + e ^{x}}

(ln (6), \frac{1}{2})

Solution steps

f^{''} (x) = \frac{6 e ^{x} ( - e ^{x} + 6 )}{( 6 + e ^{x} ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < ln (6),

Concave Downward

: ln (6) < x < \infty

Plug

x = ln (6)

into

\frac{e ^{x}}{6 + e ^{x}} : \frac{1}{2}

(ln (6), \frac{1}{2})

f (x) = 3 lo g_{3} (x + 3) + 1

f (x) = 2 x^{4 x}

f (x) = - 2 (x + 3)^{2} - 1

f (x) = lo g_{6} (2 x) + lo g_{6} (3)

f (x) = x^{2} - 7 x

What is the inflection f(x)=(e^x)/(6+e^x) ?
The inflection f(x)=(e^x)/(6+e^x) is (ln(6), 1/2)