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Homework Help: Quotient rule with additional condition

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data

    I am working on chemical reaction engineering problem and it involves some math, which I am not able to figure out...

    I have to find the residence time for maximum production, which is in the case when : (dη_p)/dτ=0

    I have to find the τ (residence time).

    2. Relevant equations


    3. The attempt at a solution

    I figure I have to use the quotient rule:



    When I use the rule, I come up with an number which is not the same as in the answers. The reason is I think that I don't know how to take into account the condition that (dη_p)/dτ=0
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 8, 2013 #2


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    Homework Helper

    The derivative has to be zero, that means an equation for τ, easy to solve. Show your further work please.

  4. May 8, 2013 #3
    When you say the derivative equals zero, do you mean this:




    and solving for τ=5 , which is the correct answer.

    However, I don't understand why g^2=0 ?
  5. May 8, 2013 #4


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    Science Advisor

    g^2 is NOT 0. What makes you think it is?
  6. May 8, 2013 #5
    I don't have any scientific reasoning behind my logic, but basically that is the only way I could see that I come up with the answer given in the book.

    If I subsitute g^2=(1+0.4τ+0.04τ^2)^2 and using the formula
    (a+b+c)^2= a^2+b^2+c^2+ 2(ab+bc+ca)

    I end up with


    What would be the next step from here?
  7. May 8, 2013 #6


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    Staff Emeritus
    Science Advisor
    Homework Helper

    If g^2 = 0, the derivative is undefined. The quantity (f'g - fg') must be 0 to satisfy the equation.
  8. May 8, 2013 #7


    Staff: Mentor

    To elaborate on what SteamKing said, the basic idea is that if a/b = 0, then a = 0. Of course, b cannot be 0.
  9. May 9, 2013 #8
    Thanks everyone!
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