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Popular >

inflection f(x)=4xe^{-x^2}

Solution

inflection points

f (x) = 4 x e^{- x^{2}}

Solution

(- \frac{3}{2}, - \frac{2 6}{e ^{\frac{3}{2}}}), (0, 0), (\frac{3}{2}, \frac{2 6}{e ^{\frac{3}{2}}})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = - \frac{3}{2}, x = 0, x = \frac{3}{2}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

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

All inflection points are in domain and not on domain edges

x = - \frac{3}{2}, x = 0, x = \frac{3}{2}

Find intervals:

Concave Downward

: - \infty < x < - \frac{3}{2},

Concave Upward

: - \frac{3}{2} < x < 0,

Concave Downward

: 0 < x < \frac{3}{2},

Concave Upward

: \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

4 x e^{- x^{2}} : - \frac{2 6}{e ^{\frac{3}{2}}}

(- \frac{3}{2}, - \frac{2 6}{e ^{\frac{3}{2}}})

Plug

x = 0

into

4 x e^{- x^{2}} : 0

(0, 0)

Plug

x = \frac{3}{2}

into

4 x e^{- x^{2}} : \frac{2 6}{e ^{\frac{3}{2}}}

(\frac{3}{2}, \frac{2 6}{e ^{\frac{3}{2}}})

(- \frac{3}{2}, - \frac{2 6}{e ^{\frac{3}{2}}}), (0, 0), (\frac{3}{2}, \frac{2 6}{e ^{\frac{3}{2}}})

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