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Math Help - Difference Quotient

  1. #1
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    Question Difference Quotient

    Hello,

    I am having a hard time understanding the difference quotient.
    f(x+h)-f(x)
    -----------
    h

    Ex: for f(x)= 8x+9

    I understand that for every x, I put in 8x+9 for it, but what do i do for the first part where it is f(x+h)? Here is where I get confused. In some examples from school it becomes (x+h)^2 . How is that possible if you are supposed to plug in 8x+9 for every x? I dont get it.

    Other problems I'm having trouble with
    f(x)= 5x^2
    f(x)= x^2+3x+9

    I'm sure with a detailed explanation, i can solve these.

    Thanks for yalls help
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by usrnme14 View Post
    Hello,

    I am having a hard time understanding the difference quotient.
    f(x+h)-f(x)
    -----------
    h

    Ex: for f(x)= 8x+9

    I understand that for every x, I put in 8x+9 for it, but what do i do for the first part where it is f(x+h)? Here is where I get confused. In some examples from school it becomes (x+h)^2 . How is that possible if you are supposed to plug in 8x+9 for every x? I dont get it.
    apparently you don't understand

    to find f(x + h) you replace all the x's in f(x) with x + h.

    if f({\color{red}x}) = 8{\color{red}x} + 9, then f({\color{red}x + h}) = 8({\color{red}x + h}) + 9 = 8x + 8h + 9

    now, you know f(x) and f(x + h), so just plug them into the difference quotient formula.

    Other problems I'm having trouble with
    f(x)= 5x^2
    f(x)= x^2+3x+9

    I'm sure with a detailed explanation, i can solve these.

    Thanks for yalls help
    try these yourself. post what you get
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  3. #3
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    I'm Lost

    I still don't get it. I'm not understanding how you got that. Could you post a solution and how you got it to just one of the problems, so i can follow it?

    Thanks,
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    New York, USA
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    Quote Originally Posted by usrnme14 View Post
    I still don't get it. I'm not understanding how you got that. Could you post a solution and how you got it to just one of the problems, so i can follow it?

    Thanks,
    how i got what? i even color coded it. all you do is wherever you see "x", you write "(x + h)" instead. that is it

    f(x)........................f(x + h)

    8x -----------------> 8(x + h)

    9x -----------------> 9(x + h)

    x^2 ---------------> (x + h)^2

    2x^2 + 3x + 2 ----> 2(x + h)^2 + 3(x + h) + 2

    is this really that confusing? why don't you try? you might pleasantly surprise yourself
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