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Two different tangents which are perpendicular?

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data
    Does the curve y=x^2 have two different tangents which are perpendicular? Does the curve y=x^3?

    3. The attempt at a solution
    I have no idea how to prove that for x^2 or x^3.
    (x^2)' =2x that is tangent at a point x
    then m = -1/2 x for another point....
    How do i prove that there is sucha point? then how about x^3?
     
  2. jcsd
  3. Nov 2, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Differentiation

    Two lines are perpendicular if and only if the product of their slopes is -1. So the question is, "are the two different values of x, say x1 and x2, such that (2x1)(2x2)= -1?"
    For the cubic, the corresponding equation is (3x12)(3x22)= -1.
     
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