What is the extreme y=3x^3e^{-x} ?

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

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extreme y=3x^3e^{-x}

extreme points

y = 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}})

f (a, b) = (9 a^{2} + 3 b^{2}) e^{(ab)^{2}}

- (x - 10) (x - 60)

f (x) = x^{4} - 24 x^{2} = x^{2} (x^{2} - 24)

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

f (x, y) = 2 x^{2} + x \cdot y^{3} - 4 y

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