What is the critical x*e^{-2x} ?

The critical x*e^{-2x} is x= 1/2

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critical x*e^{-2x}

critical points

x \cdot e^{- 2 x}

x = \frac{1}{2}

Solution steps

x e^{- 2 x}

Find where

f^{'} (x)

is equal to zero or undefined

x = \frac{1}{2}

Identify critical points not in

f (x)

domain

Domain of

x \cdot e^{- 2 x} : - \infty < x < \infty

All critical points are in domain

x = \frac{1}{2}

f (x) = - x

f (x) = 7 x + 12

\frac{x - 9}{x - 2}

4 x^{4} - 3

(3, 2), (- 11, - 3)