What is the extreme f(x)=x^6e^{-x} ?

The extreme f(x)=x^6e^{-x} is Minimum(0,0),Maximum(6,(46656)/(e^6))

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extreme f(x)=x^6e^{-x}

extreme points

f (x) = x^{6} e^{- x}

Minimum (0, 0), Maximum (6, \frac{46656}{e ^{6}})

Solution steps

f^{'} (x) = e^{- x} x^{5} (6 - x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

x^{6} e^{- x} : 0

Minimum (0, 0)

Plug

x = 6

into

x^{6} e^{- x} : \frac{46656}{e ^{6}}

Maximum (6, \frac{46656}{e ^{6}})

Minimum (0, 0), Maximum (6, \frac{46656}{e ^{6}})

What is the extreme f(x)=x^6e^{-x} ?
The extreme f(x)=x^6e^{-x} is Minimum(0,0),Maximum(6,(46656)/(e^6))