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Simple Precalculus: Average rate of change

  1. Jun 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the average rate of change:
    g(x)=1/x; x = 1, x = a

    2. Relevant equations
    (f(b)-f(a))/(b-a) = Average rate of change

    3. The attempt at a solution
    I've spent far too much time on this problem, but I know I'm making a stupid error and I just can't pin it down. So far, the steps I'm pretty confident about:

    g(1) = 1/1 = 1
    g(a) = 1/a

    Average rate of change = ((1/a)-1)/(a-1)

    According to the book the answer is -(1/a)... but I'm just not seeing it.
  2. jcsd
  3. Jun 11, 2009 #2


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    Homework Helper

    1/a-1 = (1-a)/a :wink:
  4. Jun 11, 2009 #3
    Yea, got it now. It was just as ridiculous an oversight as I had originally thought. I kept getting to the point in the problem where I had (1-a)/(a(a-1)) and going, "Oh, I can't divide those binomials!" Factor out a -1 from the numerator, cancel out the resulting binomial with the denominator and there's the answer... staring me right in the face. I'm rather embarrassed that I had so much trouble with such a simple problem, and that I forgot such a basic rule. Thanks for the help.
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