What is the monotone f(x)=(5-x)e^{-x} ?

The monotone f(x)=(5-x)e^{-x} is Decreasing:-infinity <x<6,Increasing:6<x<infinity

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monotone f(x)=(5-x)e^{-x}

monotone intervals

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

Decreasing : - \infty < x < 6, Increasing : 6 < x < \infty

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 6,

Increasing

: 6 < x < \infty

Decreasing : - \infty < x < 6, Increasing : 6 < x < \infty

What is the monotone f(x)=(5-x)e^{-x} ?
The monotone f(x)=(5-x)e^{-x} is Decreasing:-infinity <x<6,Increasing:6<x<infinity