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

The extreme f(x)=3xe^{-x} is Maximum(1, 3/e)

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extreme f(x)=3xe^{-x}

extreme

Maximum (1, \frac{3}{e})

Solution steps

Find the critical points:

x = 1

Domain of

3 x e^{- x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

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

Maximum (1, \frac{3}{e})

What is the extreme f(x)=3xe^{-x} ?
The extreme f(x)=3xe^{-x} is Maximum(1, 3/e)