What is the extreme e^{-x}(2x+1)+3 ?

The extreme e^{-x}(2x+1)+3 is Maximum(1/2 , 2/(sqrt(e))+3)

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extreme e^{-x}(2x+1)+3

extreme points

e^{- x} (2 x + 1) + 3

Maximum (\frac{1}{2}, \frac{2}{e} + 3)

Solution steps

f^{'} (x) = - e^{- x} (2 x - 1)

Find intervals:

Increasing

: - \infty < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = \frac{1}{2}

into

e^{- x} (2 x + 1) + 3 : \frac{2}{e} + 3

Maximum (\frac{1}{2}, \frac{2}{e} + 3)

What is the extreme e^{-x}(2x+1)+3 ?
The extreme e^{-x}(2x+1)+3 is Maximum(1/2 , 2/(sqrt(e))+3)