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A Quesiton on Derivatives

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Find a point P on y=x3 such that the tangent at P intersects the original curve again at point Q so that the slope of the tangent at Q is 4 times the slope of the tangent at P.


    2. Relevant equations
    y'=3x2

    and the slope of the what I think it should be a secant line=(y2-y1)/(x2-x1)

    3. The attempt at a solution

    I figured that 2P=Q because 3P2=(3/4)Q2 and then by using algebra I expressed Q in terms of P.

    I know this leads to somewhere, but im not sure what should I do next.
     
  2. jcsd
  3. Oct 23, 2011 #2

    LCKurtz

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    But P and Q are points. So P2 and Q2 don't make any sense. Try writing P = (a,a3) and Q= (c,c3) so you have two unknowns a and c. Write the equation of the tangent line at P and use the two facts that it must intersect Q and the slope condition you are given.
     
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