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

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

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

extreme points

f (x) = x^{3} \cdot 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} \cdot e^{- x} : 0

Saddle (0, 0)

Plug

x = 3

into

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

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

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

f (x) = cot (\frac{x}{2} - \frac{π}{4}) + 1

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

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

f (x) = x^{4} - 81

tan (- 2 x)

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