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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

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

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

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

- 6 = \frac{12}{- 8 - v}

f (x) = \frac{- 3 x ^{2} - 9 x}{- x + 1}

\frac{x ^{2}}{2 - x}

(0, 3), (0, 12)

- x^{2} + 4

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