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Math Help - Difference Quotient Problem

  1. #1
    Newbie StaplerPro's Avatar
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    Difference Quotient Problem

    Hello all,

    I have been doing a difference quotient problem for homework and can't seem to get it right.

    The problem is this:
    Find f(x+h)-f(x)/h where h=/=0 given the function x^2-x+4.

    By following my teacher's instructions I did this and got this answer:
    Difference Quotient Problem-differencequotientprobl.png

    However, I am told the problem is wrong, and I have tried doing it several times, and I can't seem to get the correct answer..

    Any help would be greatly appreciated. Thank you very much in advance.

    Edit:

    While looking at the problem I found a place where I made a mistake and I still got the wrong answer having taken that mistake into consideration:

    the mistake was where -(x^2-x+4) were concerned the correct way would have been -x^2+x-4 not -x^2-x-4.

    After doing that I get the answer 3x+h which is also incorrect.
    Last edited by StaplerPro; September 10th 2011 at 02:20 PM.
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  2. #2
    MHF Contributor

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    Re: Difference Quotient Problem

    You reduce to \frac{h+ h^2}{h} and say that that is equal to h. That is your mistake. \frac{h+ h^2}{h}= \frac{h(1+ h)}{h}= 1+ h (for h not equal to 0).
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  3. #3
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    Re: Difference Quotient Problem

    Quote Originally Posted by StaplerPro View Post
    Hello all,

    I have been doing a difference quotient problem for homework and can't seem to get it right.

    The problem is this:
    Find f(x+h)-f(x)/h where h=/=0 given the function x^2-x+4.

    By following my teacher's instructions I did this and got this answer:
    Click image for larger version. 

Name:	differencequotientprobl.png 
Views:	15 
Size:	22.5 KB 
ID:	22234

    However, I am told the problem is wrong, and I have tried doing it several times, and I can't seem to get the correct answer..

    Any help would be greatly appreciated. Thank you very much in advance.

    Edit:

    While looking at the problem I found a place where I made a mistake and I still got the wrong answer having taken that mistake into consideration:

    the mistake was where -(x^2-x+4) were concerned the correct way would have been -x^2+x-4 not -x^2-x-4.

    After doing that I get the answer 3x+h which is also incorrect.
    The numerator simplifies to 2xh + h^2 - h ....
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  4. #4
    Newbie StaplerPro's Avatar
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    Re: Difference Quotient Problem

    Thank you for your reply HallsofIvy, I see your logic and it makes sense, however if I put it into the homework problem, I am told that answer is also incorrect.
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  5. #5
    Newbie StaplerPro's Avatar
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    Re: Difference Quotient Problem

    Mr. fantastic, I did the first part over and I see that you are correct in that, *embarassed*.

    Does this mean if I divide it by h the answer would be .. 2x+h? I'm sorry, I'm not very good at this..

    And thank you for your reply. (:
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  6. #6
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    Re: Difference Quotient Problem

    Quote Originally Posted by StaplerPro View Post
    Mr. fantastic, I did the first part over and I see that you are correct in that, *embarassed*.

    Does this mean if I divide it by h the answer would be .. 2x+h? I'm sorry, I'm not very good at this..

    And thank you for your reply. (:
    (2xh + h^2 - h)/h does NOT equal 2x + h.
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  7. #7
    Newbie StaplerPro's Avatar
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    Re: Difference Quotient Problem

    Forgive me for asking too many silly questions here..

    Let me use a picture to explain what I'm doing (trying another way since 2x+h is incorrect):


    ? If not then should I divide the h in parenthesis by the h below as well to make it 2x-1?

    Thank you again for your reply

    Edit: The answer is 2x+h-1, thank you very much mr. fantastic!!
    Last edited by StaplerPro; September 10th 2011 at 02:54 PM.
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