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Find Intervals, where Function is Convex or Concave and Inflection Points

  1. Nov 9, 2012 #1
    1. The problem statement, all variables and given/known data
    y= (x^2 -7) e^x





    3. The attempt at a solution

    I'm trying to find inflection points by setting the second derivative=0
    I found that the derivative is:
    ##2xe^{x}+x^{2}e^{x}-7e^{x}=0##
    ##e^{x}[2x+x^{2}-7]=0##
    Then, the 2nd derivative:
    ##e^{x}[(x-1)(x+5)]=0##, then the inflection points are at x=- infinity; 1; -5.
    Where ##e^{x}=0 ##, happens when x=-infinity
    Is it correct to use - infinity as a value of x ?
     
    Last edited: Nov 9, 2012
  2. jcsd
  3. Nov 9, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    No, it's not. Basically, an inflection point x0 is a point where the behavior of f(x) changes from convex to concave (or opposite) as x increases through x0. How do you increase from values < -∞ to > -∞ (that is, how do you pass from one side of -∞ to the other)?

    RGV
     
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