What is the extreme f(x)=x^3e^{-4x} ?

The extreme f(x)=x^3e^{-4x} is Saddle(0,0),Maximum(3/4 ,(27)/(64e^3))

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

extreme

Saddle (0, 0), Maximum (\frac{3}{4}, \frac{27}{64 e ^{3}})

Solution steps

f^{'} (x) = e^{- 4 x} x^{2} (3 - 4 x)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

x^{3} e^{- 4 x} : 0

Saddle (0, 0)

Plug

x = \frac{3}{4}

into

x^{3} e^{- 4 x} : \frac{27}{64 e ^{3}}

Maximum (\frac{3}{4}, \frac{27}{64 e ^{3}})

Saddle (0, 0), Maximum (\frac{3}{4}, \frac{27}{64 e ^{3}})

What is the extreme f(x)=x^3e^{-4x} ?
The extreme f(x)=x^3e^{-4x} is Saddle(0,0),Maximum(3/4 ,(27)/(64e^3))