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

The extreme f(x)=x^3e^{-3x} is Saddle(0,0),Maximum(1, 1/(e^3))

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

extreme points

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

Saddle (0, 0), Maximum (1, \frac{1}{e ^{3}})

Solution steps

f^{'} (x) = 3 e^{- 3 x} x^{2} (1 - x)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

x^{3} e^{- 3 x} : \frac{1}{e ^{3}}

Maximum (1, \frac{1}{e ^{3}})

Saddle (0, 0), Maximum (1, \frac{1}{e ^{3}})

f (x, y) = y^{3} + 3 x^{2} y - 6 x y + 1

f (x) = \frac{1}{4} (x - 8)^{4} + \frac{17}{3} (x - 8)^{3}

f (x, y) = \frac{x}{∣ y ∣}

f (x) = x^{2} - 10 x + 21

f (x, y) = e^{x} (x^{2} + y^{2})

What is the extreme f(x)=x^3e^{-3x} ?
The extreme f(x)=x^3e^{-3x} is Saddle(0,0),Maximum(1, 1/(e^3))