What is the inflection f(x)=e^{-3.5x^2} ?

The inflection f(x)=e^{-3.5x^2} is (-1/(sqrt(7)),0.60653…),(1/(sqrt(7)),0.60653…)

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inflection f(x)=e^{-3.5x^2}

inflection points

f (x) = e^{- 3.5 x^{2}}

(- \frac{1}{7}, 0.60653 \dots), (\frac{1}{7}, 0.60653 \dots)

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - \frac{1}{7}, x = \frac{1}{7}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

e^{- 3.5 x^{2}} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = - \frac{1}{7}, x = \frac{1}{7}

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{7},

Concave Downward

: - \frac{1}{7} < x < \frac{1}{7},

Concave Upward

: \frac{1}{7} < x < \infty

Plug

x = - \frac{1}{7}

into

e^{- 3.5 x^{2}} : 0.60653 \dots

(- \frac{1}{7}, 0.60653 \dots)

Plug

x = \frac{1}{7}

into

e^{- 3.5 x^{2}} : 0.60653 \dots

(\frac{1}{7}, 0.60653 \dots)

(- \frac{1}{7}, 0.60653 \dots), (\frac{1}{7}, 0.60653 \dots)

y = 2 x^{2} + 12 x - 8

\frac{1}{x - 1} + 1

9 - 7 x^{3}

f (x) = \frac{( 3 x ^{2} - 108 )}{x + 1}

2 x + 5 y = 20

What is the inflection f(x)=e^{-3.5x^2} ?
The inflection f(x)=e^{-3.5x^2} is (-1/(sqrt(7)),0.60653…),(1/(sqrt(7)),0.60653…)