What is the inflection (x^3)/(x^3+1) ?

The inflection (x^3)/(x^3+1) is (0,0),(1/(\sqrt[3]{2)}, 1/3)

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inflection (x^3)/(x^3+1)

inflection points

\frac{x ^{3}}{x ^{3} + 1}

Solution steps

f^{''} (x) = \frac{6 x ( - 2 x ^{3} + 1 )}{( x ^{3} + 1 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - 1,

Concave Downward

: - 1 < x < 0,

Concave Upward

Concave Downward

Plug

x = 0

into

\frac{x ^{3}}{x ^{3} + 1} : 0

(0, 0)

Plug

into

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

e^{- x} - 2

\frac{- 12 x - 40}{9 x + 6}

(- 44, - 21), (43, - 32)

f (x) = 5 x^{2} + 7 x - 11

lo g_{3} (x^{2} - 4 x + 3)

What is the inflection (x^3)/(x^3+1) ?
The inflection (x^3)/(x^3+1) is (0,0),(1/(\sqrt[3]{2)}, 1/3)