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Math Help - Finding and evaluating difference quotient

  1. #1
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    Post Finding and evaluating difference quotient

    Morning Forum any help with the following would be appreciated im having issues with it
    Find the difference quotient for y = f(x) = 3x2 + 2, and evaluate it for
    (a) h = 2 (b) h = 0.2 (c) h = 0.02)
    (d) Describe what will happen as h gets smaller and smaller

    Thanks - AC-
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  2. #2
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    f(x) = 3x^2 + 2

    f(x+h) = 3(x+h)^2 + 2

    difference quotient ...

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

    I would start by expanding the expression for f(x+h)
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  3. #3
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    Quote Originally Posted by AlgebraicallyChallenged View Post
    Morning Forum any help with the following would be appreciated im having issues with it
    Find the difference quotient for y = f(x) = 3x2 + 2, and evaluate it for
    (a) h = 2 (b) h = 0.2 (c) h = 0.02)
    (d) Describe what will happen as h gets smaller and smaller

    Thanks - AC-
    Do you know what the difference quotient is? It's a means of approximating the gradient of a point on a curve.

    I'll leave you to do the research as to why, but the difference quotient is given by

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


    f(x + h) = 3(x + h)^2 + 2 = 3(x^2 + 2xh + h^2) + 2 = 3x^2 + 6xh + 3h^2 + 2

    f(x) = 3x^2 + 2.

    f(x + h) - f(x) = 6xh + 3h^2

    \frac{f(x+h) - f(x)}{h} = \frac{6xh + 3h^2}{h} = 6x + 3h.


    Now evaluate this at your given values of h and tell me what happens as h gets closer and closer to 0.
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    Quote Originally Posted by skeeter View Post
    f(x) = 3x^2 + 2

    f(x+h) = 3(x+h)^2 + 2

    difference quotient ...

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

    I would start by expanding the expression for f(x+h)
    It's actually \frac{f(x + h) - f(x)}{(x + h) - x}.
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