What is the extreme f(x)=2x^3e^{-x} ?

The extreme f(x)=2x^3e^{-x} is Saddle(0,0),Maximum(3,(54)/(e^3))

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

extreme points

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

Saddle (0, 0), Maximum (3, \frac{54}{e ^{3}})

Solution steps

Find the critical points:

x = 0, x = 3

Domain of

2 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

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

Saddle (0, 0)

Plug the extreme point

x = 3

into

2 x^{3} e^{- x} \Rightarrow y = \frac{54}{e ^{3}}

Maximum (3, \frac{54}{e ^{3}})

Saddle (0, 0), Maximum (3, \frac{54}{e ^{3}})

f (x) = x - 2 sin (x), 0 \leq x \leq 2 π

f (x) = sin (6 x)

f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x

f (x) = x^{\frac{3}{5}}

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

What is the extreme f(x)=2x^3e^{-x} ?
The extreme f(x)=2x^3e^{-x} is Saddle(0,0),Maximum(3,(54)/(e^3))