What is the inflection f(x)=e^{-2.5x^2} ?

The inflection f(x)=e^{-2.5x^2} is (-1/(sqrt(5)),0.60653…),(1/(sqrt(5)),0.60653…)

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inflection f(x)=e^{-2.5x^2}

inflection points

f (x) = e^{- 2.5 x^{2}}

(- \frac{1}{5}, 0.60653 \dots), (\frac{1}{5}, 0.60653 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - \frac{1}{5}, x = \frac{1}{5}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- 2.5 x^{2}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = - \frac{1}{5}, x = \frac{1}{5}

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{5},

Concave Downward

: - \frac{1}{5} < x < \frac{1}{5},

Concave Upward

: \frac{1}{5} < x < \infty

Plug

x = - \frac{1}{5}

into

e^{- 2.5 x^{2}} : 0.60653 \dots

(- \frac{1}{5}, 0.60653 \dots)

Plug

x = \frac{1}{5}

into

e^{- 2.5 x^{2}} : 0.60653 \dots

(\frac{1}{5}, 0.60653 \dots)

(- \frac{1}{5}, 0.60653 \dots), (\frac{1}{5}, 0.60653 \dots)

3 x^{2} + 2 x + 1

\frac{- x}{2 x - 5}

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

\frac{x - 6}{- 3 x}

sin (2) (x - \frac{π}{2}) + 1

What is the inflection f(x)=e^{-2.5x^2} ?
The inflection f(x)=e^{-2.5x^2} is (-1/(sqrt(5)),0.60653…),(1/(sqrt(5)),0.60653…)