What is the inflection f(x)=-2xe^{-3x} ?

The inflection f(x)=-2xe^{-3x} is (2/3 ,-4/(3e^2))

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inflection f(x)=-2xe^{-3x}

inflection points

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

(\frac{2}{3}, - \frac{4}{3 e ^{2}})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = \frac{2}{3}

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

- 2 x e^{- 3 x} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = \frac{2}{3}

Find intervals:

Concave Upward

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

Concave Downward

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

Plug

x = \frac{2}{3}

into

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

(\frac{2}{3}, - \frac{4}{3 e ^{2}})

f (x) = 3 x^{2} - 6

f (x) = - \frac{4}{x ^{2} - 3 x + 6}

3 x + 6 y = 5, at

y = 3 - 5 x

(2, 3), (1, 0)

What is the inflection f(x)=-2xe^{-3x} ?
The inflection f(x)=-2xe^{-3x} is (2/3 ,-4/(3e^2))