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Homework Help: A Derivative Question

  1. Sep 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Let f(x) be the function 6x2-3x+11 . Then the quotient f(6+h)-f(6) / h can be simplified to ah+b for what value of a and what value of b?

    2. Relevant equations

    I think I need to simplify the quotient above.

    3. The attempt at a solution

    I know that a=6. I'm not sure what b is supposed to be, nor am I sure what the question is asking me exactly. Perhaps if someone could clarify what I'm supposed to be looking for, it'd give me a push in the right direction.

  2. jcsd
  3. Sep 10, 2010 #2


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    Staff Emeritus
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    Gold Member

    Have you tried evaluating f(6+h)-f(6) / h and seeing what you get?
  4. Sep 10, 2010 #3
    I would get 1 (one), correct?
  5. Sep 10, 2010 #4


    Staff: Mentor

    No, you're way off. You have the formula for the function, so evaluate [f(6 + h) - f(6)]/h.
  6. Sep 10, 2010 #5
    OK, I set up the expression as (6+h)^2-3(6+h)+11-6 / h

    From this, I got 6h+272

    Is this the correct method?
  7. Sep 10, 2010 #6


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    Sort of, except you are making a lot of mistakes. It's 6*(6+h)^2-3*(6+h)+11-f(6) in the numerator. And f(6) isn't 6.
  8. Sep 10, 2010 #7
    I was working at this problem over dinner with friends and one of my friend's girlfriend happened to see me. She's a math tutor and she showed me the mistakes I was making. I know now that it works out to 6h+69. Thank you all for the added help; I am sorry for being frustrating with my obvious mistakes. :/
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