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Instantaneous rate of change homework

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    For the function f(x)=3x^2-1, for what x values is the instantaneous rate of change equal to the average rate of change on the interval [1,3]


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 26, 2009 #2
    Re: Derivatives

    1) first find the average rate of change on the interval (1,3)

    2) set that number equal to the derivative of the function and solve for x


    1) Finding the avg rate of change over the interval 1,3

    f(1) = 2
    f(3) = 26

    so we have (1,2) and (3,26)
    the slope give the rate of change so to find the slope between these points
    we use the slope formula which gives us 12

    2) f `(x) = 3x^2+1

    average rate of change = 6x

    12 = 6x

    x = 2

    so when x = 2 in the instantaneous rate of change, it equals the average rate on the
    interval [1,3]. notice its between 1 and 3.
     
  4. Apr 26, 2009 #3
    Re: Derivatives

    Just to add you might want to look-up the mean value theorem.
     
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