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Finding rate of change formulas with the given information

  1. Apr 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Let Q(t)=t2. Find a formula for the average rate of change (ROC) of Q over the interval [1, t] and use it to estimate the instantaneous ROC at t = 1.


    2. Relevant equations

    For x1 ≠ x0, the average rate of change of y with respect to x over [x0, x1] is the ratio

    Average ROC = Δf/Δx = f(x1) - f(x0) / x1 - x2

    Finding the instantaneous rate of change is basically the same as finding the avg ROC, except instead of using the intervals that are given (say [7, 10] for example) they give you one number, and you create your own intervals by choosing numbers extremely close to that given number (say [7, 7.01] or [7, 6.99] etc.)

    3. The attempt at a solution

    All I can think of is plugging in the intervals as with previous problems. Plugging t into t gives you t.

    Plugging 1 into t gives you one squared which is one. Then you subtract those two to get

    t2 - 1. The bottom portion which is x1 - x2 would look just like t - 1.

    So maybe t squared minus one over t minus one is the formula? I suppose I could factor it out to

    (t +1)(t - 1) / (t - 1) cancel out the expressions and get t + 1. So t + 1 would be the requested formula for the average rate of change? To get instantaneous ROC at t = 1, wouldn't I just plug one into "t" and get 2?

    That can't be right
     
    Last edited: Apr 4, 2013
  2. jcsd
  3. Apr 4, 2013 #2
    Anyone have some ideas?
     
  4. Apr 5, 2013 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It looks right.

    ehild
     
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