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Intervals of increase/decrease with a exponential function

  1. Jun 16, 2006 #1
    find the intervals of increase and decrease of f(x) = e3x + e-2x.

    f'(x) = 3e3x - 2e-2x
    I set f'(x) = 0 to find the critical numbers:
    3e3x = 2e-2x
    3 ln e3x = 2 ln e-2x
    9x = -4x
    x = 0, which is obviously wrong, (3e^0 - 2e^0 = 1). I found out that I had to combine the two terms using a common denomintor, and I got the right answer.

    But why did my original method fail?
     
  2. jcsd
  3. Jun 16, 2006 #2

    Hootenanny

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    Quite simply because;
    [tex]3\ln|e^{3x}| \neq \ln |3e^{3x}|[/tex]
     
  4. Jun 16, 2006 #3
    ahh.... i feel so stupid.. i hate when i make simple mistakes and mix formulas up. :uhh:
     
  5. Jun 16, 2006 #4

    Hootenanny

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    I did a very similar thing in an exam yesterday, I was sat there for fifteen mintues trying to figure out where I had gone wrong, then I realised, I had differentiated instead of integrated :blushing:, it was a good job I realised before the end of the test! :rolleyes:
     
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