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Implicitly defined parametrizations

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data
    x^3+2t^2=9, 2y^3-3t^2=4, t=2
    find the slope of the curve at the given value of t

    2. Relevant equations



    3. The attempt at a solution
    i know dy/dx=(dy/dt)/(dx/dt) for parametrized curves
    but how do i use implicit differentiation on parametrized curves?
    i tried d/dt(2y^3-3t^2)=d/dt(4)
    =6y^2*dy/dt-6t=0
    =6y^2*dy/dt=6t
    =dy/dt=t/y^2 ? but shouldnt dy/dt be defined in t's only? im confused
     
  2. jcsd
  3. Nov 6, 2011 #2

    SammyS

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    Find dx/dt in a similar fashion. Also find x & y, when t = 2.

    Then combine the results: [itex]\displaystyle \frac{dy/dt}{dx/dt}[/itex] will have t cancel out, in this case.
     
  4. Nov 6, 2011 #3
    i thought about trying that out before asking for help
    but i kept thinking there had to be an easier way
    well thanks for the help
     
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