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

The extreme f(x)=3x^3e^{-x} is Saddle(0,0),Maximum(3,(81)/(e^3))

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

extreme points

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

Saddle (0, 0), Maximum (3, \frac{81}{e ^{3}})

Solution steps

Find the critical points:

x = 0, x = 3

Domain of

3 x^{3} e^{- x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug the extreme point

x = 0

into

3 x^{3} e^{- x} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = 3

into

3 x^{3} e^{- x} \Rightarrow y = \frac{81}{e ^{3}}

Maximum (3, \frac{81}{e ^{3}})

Saddle (0, 0), Maximum (3, \frac{81}{e ^{3}})

y = 100 + \frac{1}{2} x + \frac{1800}{x}

f (x) = x^{3} - 15 x

f (x) = x^{3} - 3 x, - 1 \leq x \leq 2

\frac{d}{d r} (4 k^{\frac{3}{2}} (\frac{r}{w}))

f (x) = x + 10 1 - x, - 2 \leq x \leq 5

What is the extreme f(x)=3x^3e^{-x} ?
The extreme f(x)=3x^3e^{-x} is Saddle(0,0),Maximum(3,(81)/(e^3))