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Homework Help: Intermediate Value Thoerum?

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that the equation e^x = x + 2 had exactly two solutions. Explain your reasoning.

    2. Relevant equations

    Okay so I guess I'm using the intermediate value theorum and proving that f(a)f(b) < 0 we can find a c and d such that f(c) = 0 and f(d) = 0 so that by collorary it's true. This is an issue because I don't have boundaries for my function...

    3. The attempt at a solution

    create a function: f(x) = e^x - x - 2
    and that's about as far as I got. I'm assuming I arbitarily select an interval and use that? Are there rule that I should follow though?
  2. jcsd
  3. Nov 24, 2007 #2


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    Homework Helper

    I would believe you should select some values and check for a sign change...
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