What is the inflection f(x)=e^{-x^3} ?

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

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inflection f(x)=e^{-x^3}

inflection points

f (x) = e^{- x^{3}}

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- x^{3}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

Concave Upward

Plug

x = 0

into

e^{- x^{3}} : 1

(0, 1)

Plug

into

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

\frac{2}{x} - 7

f (x) = 3

3 - 2 x

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

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