What is the extreme f(x)=x^3e^{-x} ?

The extreme f(x)=x^3e^{-x} is Saddle(0,0),Maximum(3,(27)/(e^3))

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

extreme points

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

Saddle (0, 0), Maximum (3, \frac{27}{e ^{3}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

x^{3} e^{- x} : 0

Saddle (0, 0)

Plug

x = 3

into

x^{3} e^{- x} : \frac{27}{e ^{3}}

Maximum (3, \frac{27}{e ^{3}})

Saddle (0, 0), Maximum (3, \frac{27}{e ^{3}})

\frac{1}{x + 4}

\frac{x - 7}{12 x + 2}

x + 3 - 2

f (x) = - \frac{5}{x}

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

What is the extreme f(x)=x^3e^{-x} ?
The extreme f(x)=x^3e^{-x} is Saddle(0,0),Maximum(3,(27)/(e^3))