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

The extreme f(x)=(x-3)*e^{-x} is Maximum(4, 1/(e^4))

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

extreme points

f (x) = (x - 3) \cdot e^{- x}

Maximum (4, \frac{1}{e ^{4}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 4

into

(x - 3) \cdot e^{- x} : \frac{1}{e ^{4}}

Maximum (4, \frac{1}{e ^{4}})

What is the extreme f(x)=(x-3)*e^{-x} ?
The extreme f(x)=(x-3)*e^{-x} is Maximum(4, 1/(e^4))