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Maximum/Minimum-Check Please?

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].


    2. Relevant equations



    3. The attempt at a solution
    f'(x)= 2x*(e^(-x)) - (e^(-x)*(x^2))
    f'(x)= x*e^(-x) (2- x)
    Solve for zero, for critical points? I got two solutions: x=0 or x= 2

    Plugging these two critical points and the endpoints on the interval back into f(x), I get:
    (0, 0) - Minimum
    (2, 4/(e^2) )
    (-10, 100*(e^10) ) - Maximum
    (10, 100/(e^10) )

    Is this right? Thank you.
     
  2. jcsd
  3. Jun 13, 2013 #2

    Mark44

    Staff: Mentor

    You don't "solve for zero", but I know what you mean - Set f' = 0 and solve that equation.
    Your max and min look OK, but check this point (10, 100/(e^10) ).
     
  4. Jun 13, 2013 #3
    Okay, I'll make sure. Thank you!
     
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