What is the inflection e^{-x^2} ?

The inflection e^{-x^2} is (-1/(sqrt(2)), 1/(sqrt(e))),(1/(sqrt(2)), 1/(sqrt(e)))

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inflection e^{-x^2}

inflection points

e^{- x^{2}}

(- \frac{1}{2}, \frac{1}{e}), (\frac{1}{2}, \frac{1}{e})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - \frac{1}{2}, x = \frac{1}{2}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- x^{2}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = - \frac{1}{2}, x = \frac{1}{2}

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{2},

Concave Downward

: - \frac{1}{2} < x < \frac{1}{2},

Concave Upward

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

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

(- \frac{1}{2}, \frac{1}{e})

Plug

x = \frac{1}{2}

into

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

(\frac{1}{2}, \frac{1}{e})

(- \frac{1}{2}, \frac{1}{e}), (\frac{1}{2}, \frac{1}{e})

f (x) = \frac{x ^{2} - 9}{x ^{2} - 3 x + 2}

4 x + 2 y = 8

- - x + 2

f (x) = x^{4} + 3 x^{3}

f (x) = \frac{3 x ^{3} + 2 x + 2}{2 x ^{3} + 5 x - 5}

What is the inflection e^{-x^2} ?
The inflection e^{-x^2} is (-1/(sqrt(2)), 1/(sqrt(e))),(1/(sqrt(2)), 1/(sqrt(e)))