Find the Extreme Values of the Function and Where They $$y = x ^ { 2 } e ^ { - x } + 2 x e ^ { - x }$$

Multiple Choice

Find the extreme values of the function and where they occur.
- $$y = x ^ { 2 } e ^ { - x } + 2 x e ^ { - x }$$

A) Minimum value is $2 e ^ { \sqrt { 2 } } ( 1 - \sqrt { 2 } )$ at $x = - \sqrt { 2 }$ ; maximum value is $2 e ^ { - \sqrt { 2 } } ( 1 + \sqrt { 2 } )$ at $x = \sqrt { 2 }$ .
B) Minimum value is $2 e \sqrt { 2 } ( 1 - \sqrt { 2 } )$ at $x = - \sqrt { 2 }$ ; no maximum value.
C) Maximum value is $2 e ^ { - \sqrt { 2 } } ( 1 + \sqrt { 2 } )$ at $x =$ ; no minimum value.
D) None