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Popular >

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

Solution

extreme points

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

Solution

Minimum (4, - \frac{1}{e ^{4}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 4

into

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

Minimum (4, - \frac{1}{e ^{4}})

Graph

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Frequently Asked Questions (FAQ)

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