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Math Help - Stuck with a Binomial using the Difference Quotient

  1. #1
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    Stuck with a Binomial using the Difference Quotient

    The problem is:

    f(x)= -5+5x^2

    I already know that it will end as 10x (it's derivative by the way).

    But using the difference quotient:

    \frac{f(x+h)-f(x)}{h}

    I'm told that,


    f(x)= -5+5x^2

    Can be written in the form

    Ah+Bx+C

    Using the Calculus short cuts. I find that "B" is (10) and I find that "C" is (0)

    However I don't know what what "A" is.

    And when I do it long hand, I get stuck at this point.

    \frac{5(2x^2+2xh+h^2)}{h}

    How do I get "10x" from that above and find "A"?
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  2. #2
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    Quote Originally Posted by Zanderist View Post
    The problem is:

    f(x)= -5+5x^2

    I already know that it will end as 10x (it's derivative by the way).

    But using the difference quotient:

    \frac{f(x+h)-f(x)}{h}

    I'm told that,


    f(x)= -5+5x^2

    Can be written in the form

    Ah+Bx+C

    Using the Calculus short cuts. I find that "B" is (10) and I find that "C" is (0)

    However I don't know what what "A" is.

    And when I do it long hand, I get stuck at this point.

    \frac{5(2x^2+2xh+h^2)}{h}

    How do I get "10x" from that above and find "A"?
    I am supposing that the full question is asking you to find the derivative with the difference quotient?

    Something to keep in mind is that the secondary form Ah+Bx+C may come from plugging into the quotient. I prefer to use the function itself.

    Considering your function is f(x) = -5 + 5x^2

    Plug in for f(x+h) = -5 + 5(x+h)^2; This goes into your difference quotient. Expand and simplify.
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  3. #3
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    I figured out what I had done wrong.

    I didn't distribute the negative sign fully.

    "A" for this problem is (5).
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