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Average rate of change help please

  1. Mar 15, 2007 #1
    1. The problem statement, all variables and given/known data

    For the function g(t) = 1/(3t-2) determine the average rate of change between the values t = 0 and t = a + 1

    2. Relevant equations

    ARoC formula : f(b) - f(a) over b-a

    3. The attempt at a solution

    So I think I am doing it right but can only get so far and then get stuck.

    I set it up : 1/3(a+1)-2 (-) 1/3(0)-2 all over a+1-0
    I calculate and get : 1/3a+1 (+) 1/2 all over a+1
    I get a common denominator to add 1/3a+1 (+) 1/2 : 2/6a+2 (+) 3a+1/6a+2 all over a+1
    and then I am not sure, or even what I have is close to coming correct. Please help. :smile:
  2. jcsd
  3. Mar 15, 2007 #2


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    Staff Emeritus
    Science Advisor

    I would prefer you used parentheses to clarify! f(0)= -1/2 certainly and
    f(a+1)= 1/(3(a+1)-2)= 1/(3a+1) so f(a+1)- f(0)= 1/(3a+1)+ 1/2. As you say, the common denominator is 2(3a+1)= 6a+ 2.

    2/(6a+2)+ (3a+1)/(6a+2)= (3a+3)/(6a+2)= 3(a+1)/(6a+2). It's easy to divide that by a+1.
  4. Mar 15, 2007 #3
    :redface: Sorry, Ok, I made it harder than it was I think, for the final answer you get : 3/(6a+2) :) ??
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