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Math Help - derivative/tangent line words!

  1. #1
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    derivative/tangent line words!

    In the figure above, line L is tangent to the graph of y=1/x^2 at point P, with coordinates (w, 1/w^2) where w>0. Point Q has coordinates (w,0). Line L crosses the x axis at the point R, with coordinates (k,0)
    a)Find the value of k when w=3

    b) for all w>0 find k in terms of w.

    c) Suppose that w in increasing at the constant rate of 7 units per second. When w=5, what is the rate of change of k with respect to time?

    d) Suppose that w increasing at the constant rate of 7 units per second. When w=5 what is the rate of change of the area of PQR with respect to time?
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  2. #2
    MHF Contributor
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    Hello

    Let f(x)=1/x
    f'(x)=-2/x^3

    Equation of tangent line to the graph at point P is
    y=f'(w) (x-w) + f(w)

    y=-\frac{2}{w^3}x+\frac{3}{w^2}

    Tangent line is crossing x axis at (k,0) such as
    0=-\frac{2}{w^3}k+\frac{3}{w^2}

    k=\frac{3w}{2}
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