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Solving derivative of exponential function

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    -Find the intervals on which f is increasing or decreasing
    -Find the local maximum and minimum values of f
    -Find the intervals of concavity and the inflection points
    f(x)=xex
    f'(x)= ex+xex
    then I must solve for x when the function equals zero to find my critical numbers
    2x+ln(x)=0

    3. The attempt at a solution

    The problem is I dont know how to get rid of the ln() to solve for x. Not that it would help all my terms have x's. so how would I find the critical number of this function? or is their only one, zero? zero because ln()is undefined at zero
     
  2. jcsd
  3. Nov 18, 2009 #2
    This tells you where the logarithm of the derivative is zero, which is not what you were asked for. Instead try

    [tex] f'(x) = (1+x)e^x = 0 [/tex] if [tex] e^x = 0 [/tex] or ...
     
  4. Nov 21, 2009 #3
    x1=-1
    If I try and solve e^x for zero i get x DNE so how do I find out where the critical point is?
     
  5. Nov 21, 2009 #4
    or is -1 the only critical number?
     
  6. Nov 21, 2009 #5
    Yes, x = -1 is the only critical point since ex is never 0.
     
  7. Nov 21, 2009 #6
    thank you
     
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