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Popular Functions >

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

Solution

inflection points

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

Solution

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

Solution steps

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

Find intervals:

Concave Downward

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

Concave Upward

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

Plug

x = \frac{2}{3}

into

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

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

Graph

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Frequently Asked Questions (FAQ)

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