Find all points of inflection of the function g(x)=x^2 e^{-x}

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blogpolisft · Accepted Answer

g  (  x  )  =      x    2        e          −      x              g    ′    (  x  )  =      x    2    (  −      e          −      x        )  +      e          −      x        (  2  x  )    =  −      x    2        e          −      x        +  2  x      e          −      x              g    ′    (  x  )  =      e          −      x        [  −      x    2    +  2  x  ]    g  &quot;  (  x  )  =      e          −      x        [  −  2  x  +  2  ]  +  [  −      x    2    +  2  x  ]  [  −      e          −      x        ]    =      e          −      x        [  −  2  x  +  2  +      x    2    −  2  x  ]    g  &quot;  (  x  )  =      e          −      x        [      x    2    −  4  x  +  2  ]    g  &quot;  (  x  )  =      e          −      x        [  (  x  −  (  2  +      2    )  )  (  x  −  (  2  −      2    )  )  ]        e          −      x        &amp;gt;  0           ∀  x  ∈  Rpoints of infleetion of g(x) where g&quot;(x) changes there implies that  [  x  =  2  −      2    ,  2  +      2    ] here g&quot;(x) changes sign from

Find all points of inflection of the function g(x)=x^2 e^(-x)

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New Questions in Calculus 1