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Homework Help: Finding the slope of a curve at a point.

  1. Apr 5, 2010 #1
    The surface given by x = x^2 - y^2 is cut by a plane give by y = 3x. producing a curve in the plane. Find the slope of this curve at the ppoint (1,3,-8)

    A) 3
    B) -16
    C) - 8sqrt(2/5)
    D) 0
    E) 18/sqrt(10)

    So we want to look at this curve when y = 3x. Then x = x^2 -y^2 becomes x = x^2 - (3x)^2 which gives x = x^2 - 9x^2.

    So we have x = -8x^2 or -8x^2 - x = 0.

    The derivative is then - 16x - 1. At the point (1,3,-8) we should should have the derivative equal to
    -17 which is not a choice..

    Can someone tell me if I did something wrong.
  2. jcsd
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