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Homework Help: Rate of change question

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Find any and all points inside the interval (0,3) where the instantaneous rate of change of f equals the average rate of change of f over the interval [0,3], for the equation

    f(x) = 4x^2 - x^3

    2. Relevant equations

    3. The attempt at a solution

    Not really sure how to do this. How do I find the average rate of change over that interval? I was thinking take the derivative:

    f'(x) = 8x - 3x^2

    plugging in 0 and 3 to get f'(0) = 0, and f'(3) = -3. So the average rate of change would be

    And then saying

    -1.5 = = 8x - 3x^2? I don't know, gah. How do I solve this problem?
  2. jcsd
  3. Sep 12, 2010 #2
    Based on how I see things, you're quite nearly there! You've just ended up with a quadratic equation, now what do you do?
  4. Sep 13, 2010 #3
    Derivatives are the instantaneous rate of change. Your book should have a formula (a very familiar looking formula) for average rates of change.
  5. Sep 13, 2010 #4


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    Homework Helper

    No, what you've written is not the "average rate of change". The average rate of change of a function f over the interval [a; b] should be calculated as follow:

    [tex]\frac{f(b) - f(a)}{b - a}[/tex]

    Hopefully, you can go from there, right? :)
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