What is the inflection f(x)=ln(1+x^3) ?

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

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inflection f(x)=ln(1+x^3)

inflection points

f (x) = ln (1 + x^{3})

Solution steps

f^{''} (x) = \frac{3 ( 2 x - x ^{4} )}{( 1 + x ^{3} ) ^{2}}

Find intervals:

Concave Downward

: - 1 < x < 0,

Concave Upward

Concave Downward

Plug

x = 0

into

ln (1 + x^{3}) : 0

(0, 0)

Plug

into

ln (1 + x^{3}) : ln (3)

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

y = \frac{1}{4} x - 3

x + y = 3

(- 2, 7.7), (3, - 2.3)

f (x) = 1 - 4 - x^{2}

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