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Popular >

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

Solution

inflection points

\frac{e ^{x}}{3 + e ^{x}}

Solution

(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})

Popular Examples

domain of sqrt(x-1)sqrt(1-x)domain

x - 1 1 - x

domain of (x+4)/(x^2-25)domain

\frac{x + 4}{x ^{2} - 25}

inverse of f(x)=(x-3)^2-4 inverse

f (x) = (x - 3)^{2} - 4

inverse of f(x)=-2cos(3x)inverse

f (x) = - 2 cos (3 x)

asymptotes of f(x)=(x^2+7x+8)/(x+3)asymptotes

f (x) = \frac{x ^{2} + 7 x + 8}{x + 3}

Frequently Asked Questions (FAQ)

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