What is the inflection e^{-1.5x^2} ?

The inflection e^{-1.5x^2} is (-1/(sqrt(3)),0.60653…),(1/(sqrt(3)),0.60653…)

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inflection e^{-1.5x^2}

inflection points

e^{- 1.5 x^{2}}

(- \frac{1}{3}, 0.60653 \dots), (\frac{1}{3}, 0.60653 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - \frac{1}{3}, x = \frac{1}{3}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- 1.5 x^{2}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = - \frac{1}{3}, x = \frac{1}{3}

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{3},

Concave Downward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Upward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

e^{- 1.5 x^{2}} : 0.60653 \dots

(- \frac{1}{3}, 0.60653 \dots)

Plug

x = \frac{1}{3}

into

e^{- 1.5 x^{2}} : 0.60653 \dots

(\frac{1}{3}, 0.60653 \dots)

(- \frac{1}{3}, 0.60653 \dots), (\frac{1}{3}, 0.60653 \dots)

3 - e^{2 x}

f (x) = \frac{( x + 9 )}{x ^{2} + 4 x}

x^{5} - 4 x^{3}

f (x) = x^{3} - x^{2} - x - 10

f (- 1) = \frac{x - 1}{x + 1}

What is the inflection e^{-1.5x^2} ?
The inflection e^{-1.5x^2} is (-1/(sqrt(3)),0.60653…),(1/(sqrt(3)),0.60653…)