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Average rate of change

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data
    I have just started my first ever calculus course, and I'm having a little trouble with a simple rate of change problem.

    It says: Find the average rate of change of the given function between the following pairs of x-values.

    The given function is f(x) = x2+ x
    The given values are x=1 and x=3


    2. Relevant equations
    Aren't I supposed to make use of the equation f(x+h) - f(x) / h ?
    I don't really understand what h is supposed to be.


    3. The attempt at a solution
    I checked what the answer should be and it shows: f(3) - f(1) / 2 = 12-2 / 5 = 5

    I understand the algebra and how it equates to the answer 5, but where did the two in the denominator come from? I feel like I'm not understanding some fundamental aspect of this problem and rates of change in general.
     
  2. jcsd
  3. Jan 23, 2010 #2
    To find the average rate of change between point (a, f(a)) and (b, f(b)), you use
    (f(b) - f(a))/(b - a). This is basically the same as finding the slope between two points m = (y2 - y1)/(x2 - x1), which you should be familiar with.

    There's really no point in using the difference quotient (f(x+h) - f(x))/h, which is an expression, not an equation, for this problem.
     
  4. Jan 23, 2010 #3
    Oh, ok. That makes sense. For some reason the equation you mentioned I should use isn't shown in my book.
     
  5. Jan 24, 2010 #4

    Mark44

    Staff: Mentor

    The expression Bohrok mentioned, namely (f(b) - f(a))/(b - a). An equation has an = sign between two expressions.
     
  6. Jan 24, 2010 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    And, taking h= b-a, the difference between the two points, b= a+ h so the formula you cite, (f(a+h)- f(a))/(h)f(b)- f(a)/(b- a), becomes (f(b)- f(a))/(b- a).
     
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