What is the inflection f(x)=e^{-0.5x^2} ?

The inflection f(x)=e^{-0.5x^2} is (-1,0.60653…),(1,0.60653…)

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inflection f(x)=e^{-0.5x^2}

inflection points

f (x) = e^{- 0.5 x^{2}}

(- 1, 0.60653 \dots), (1, 0.60653 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - 1, x = 1

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- 0.5 x^{2}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = - 1, x = 1

Find intervals:

Concave Upward

: - \infty < x < - 1,

Concave Downward

: - 1 < x < 1,

Concave Upward

: 1 < x < \infty

Plug

x = - 1

into

e^{- 0.5 x^{2}} : 0.60653 \dots

(- 1, 0.60653 \dots)

Plug

x = 1

into

e^{- 0.5 x^{2}} : 0.60653 \dots

(1, 0.60653 \dots)

(- 1, 0.60653 \dots), (1, 0.60653 \dots)

f (x) = \frac{5}{x + 4}

f (x) = 6 sec (x)

f (x) = 4 (x^{\frac{1}{5}} - 5) + 10

y = \frac{3}{x ^{2} - 49}

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

What is the inflection f(x)=e^{-0.5x^2} ?
The inflection f(x)=e^{-0.5x^2} is (-1,0.60653…),(1,0.60653…)