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Math Help - Slope of a polynomial function

  1. #1
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    Slope of a polynomial function

    Hello Friends,
    I need help on this problem
    Directions: use equation one to find g '(x) [g '(x) is the slope]
    equation one :
    g' (x) = lim h->0 g(x+h) - g(x) all over h.
    Then it says:
    Recall the Difference quotient D.Q. = g(x+h) - g(x) all over h

    The actual problem is g(x) = 3xsquared - 2x
    sorry about the squared. I couldn't put a little two
    Thanks,
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  2. #2
    MHF Contributor
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    France
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    Quote Originally Posted by xArtist545 View Post
    Hello Friends,
    I need help on this problem
    Directions: use equation one to find g '(x) [g '(x) is the slope]
    equation one :
    g' (x) = lim h->0 g(x+h) - g(x) all over h.
    Then it says:
    Recall the Difference quotient D.Q. = g(x+h) - g(x) all over h

    The actual problem is g(x) = 3xsquared - 2x
    sorry about the squared. I couldn't put a little two
    Thanks,
    Hi

    g(x) = 3x^2 - 2x

    \frac{g(x+h) - g(x)}{h} = \frac{\left(3(x+h)^2 - 2(x+h)\right) - \left(3x^2 - 2x\right)}{h}

    Expand

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

    Therefore g'(x) = \lim_{h \rightarrow 0} \frac{g(x+h) - g(x)}{h} = 6x - 2
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  3. #3
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    thanks
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