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Popular >

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}})

Popular Examples

domain of sqrt(x^2-1)domain

x^{2} - 1

domain of f(x)=x^2-7x+10 domain

f (x) = x^{2} - 7 x + 10

inverse of f(x)=4x^3-2 inverse

f (x) = 4 x^{3} - 2

range of f(x)=7+(8+x)^{1/2}range

f (x) = 7 + (8 + x)^{\frac{1}{2}}

range of y=\sqrt[3]{x+8}range

Frequently Asked Questions (FAQ)

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