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

question 50

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

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