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Derivative problem

  1. Dec 24, 2009 #1
    1. The problem statement, all variables and given/known data
    A plane starts its descent from height y=h at x =-L to land at (0,0). Choose a, b, c, d so its landing path y=ax^3 + bx^2 + cx + d is smooth.With dx/dt=V=constant, find dy/dt and d2y/dt2 at x=0 and x =-L. (To keep d2y/dt2 small, a coast-to-coast plane starts down L>100 miles from the airport.)

    3. The attempt at a solution
    For a smooth landing the derivative must be negative and 0 at x=0.
    y'=3ax^2+2bx+c < 0
    d must be 0 because y(0)=0.
    second derivative must be > 0.
    y''=6ax+2b >0

    And that's as far as I get. I'd appreciate any tips and can someone explain to me how dx/dt can be constant? And how do I find dy/dt?
  2. jcsd
  3. Dec 25, 2009 #2


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    Science Advisor
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    Merry Christmas!

    Hi kristo! :smile:

    Think of the curve as a hillside … the driver can drive at whatever speed he likes.

    And to find dy/dt, use the chain rule. :wink:
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