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Math Help - Slope of tangent line

  1. #1
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    Slope of tangent line

    I was wondering if someone could check my work. Here's my problem:

    Find the slopes of the tangent line to the curve y=x^3-3x at the points where x=-2,-1,0,1,2.

    So m_{tan}=\frac{[(c+h)^3-3(c+h)]-(c^3-3c)}{h}

    =\frac{(c^3+3c^2h+3ch^2+h^3)-3c-3h-c^3+3c)}{h}

    =\frac{3c^2h+3ch^2-3h+h^3}{h}

    =\frac{h(3c^2+3ch-3+h^2)}{h}

    lim h->0 3c^2+3ch-3+h^2=3c^2-3

    so at x=-2, m_{tan}=9
    x=-1, m_{tan}=0
    x=0, m_{tan}=-3
    x=1, m_{tan}=0
    x=2, m_{tan}=9

    Thank you for any help!
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  2. #2
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