What is the extreme f(x)=x^4e^{-x} ?

The extreme f(x)=x^4e^{-x} is Minimum(0,0),Maximum(4,(256)/(e^4))

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extreme f(x)=x^4e^{-x}

extreme

Minimum (0, 0), Maximum (4, \frac{256}{e ^{4}})

Solution steps

f^{'} (x) = e^{- x} x^{3} (4 - x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

x^{4} e^{- x} : 0

Minimum (0, 0)

Plug

x = 4

into

x^{4} e^{- x} : \frac{256}{e ^{4}}

Maximum (4, \frac{256}{e ^{4}})

Minimum (0, 0), Maximum (4, \frac{256}{e ^{4}})

What is the extreme f(x)=x^4e^{-x} ?
The extreme f(x)=x^4e^{-x} is Minimum(0,0),Maximum(4,(256)/(e^4))