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Math Help - Difference Quotient Question

  1. #1
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    Exclamation Difference Quotient Question

    I could really use some help...a littel confused. I know that the difference quotient is f(x+h)-f(x)/h

    The question in the assignment asked me to use the difference quotient to evaluate f(x)= x^2+13

    this is how i did it, could you please let me know where I went wrong...

    (x+h)(x+h)-x^2+13/h

    x^2 +2hx+h^2-x^2 +13/h
    the two x^2 are cancelled
    the h's cancel, leaving 2x+h+13/2
    my final anwer was 2x+h+13/h
    I didn't get it correct and im not sure where I went wrong...
    Thanks!
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  2. #2
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    Quote Originally Posted by epetrik View Post
    I could really use some help...a littel confused. I know that the difference quotient is f(x+h)-f(x)/h

    The question in the assignment asked me to use the difference quotient to evaluate f(x)= x^2+13

    this is how i did it, could you please let me know where I went wrong...

    (x+h)(x+h)-x^2+13/h
    1. f(x+h)= (x+h)^2+ 13, not (x+h)^2= (x+h)(x+h)
    2. -f(x)= -(x^2+ 13)= -x^2- 13, not -x^2+ 13

    x^2 +2hx+h^2-x^2 +13/h
    the two x^2 are cancelled
    the h's cancel, leaving 2x+h+13/2
    my final anwer was 2x+h+13/h
    I didn't get it correct and im not sure where I went wrong...
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  3. #3
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    Quote Originally Posted by epetrik View Post
    I could really use some help...a littel confused. I know that the difference quotient is f(x+h)-f(x)/h

    The question in the assignment asked me to use the difference quotient to evaluate f(x)= x^2+13

    this is how i did it, could you please let me know where I went wrong...

    (x+h)(x+h)-x^2+13/h

    x^2 +2hx+h^2-x^2 +13/h
    the two x^2 are cancelled
    the h's cancel, leaving 2x+h+13/2
    my final anwer was 2x+h+13/h
    I didn't get it correct and im not sure where I went wrong...
    Thanks!
    This is what I came up with:

    f(x)=x^2+13

    f(x+h)=(x+h)^2

    \frac{\Delta y}{\Delta x}=\frac{f(x+h)-f(x)}{h}=\frac{[(x-h)^2+13]-(x^2+13)}{h}=

    \frac{x^2+2xh+h^2+13-x^2-13}{h}=\frac{h^2+2xh}{h}=\frac{h(h+2x)}{h}=\boxed{  h+2x}
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