Point on a Curve

  1. jgens

    jgens 1,621
    Gold Member

    1. The problem statement, all variables and given/known data

    A particle moves along a path described by y = 4 - x^2. At what point along the curve are x and y changing at the same rate

    2. Relevant equations

    Simple equations regarding derivatives.

    3. The attempt at a solution

    It's been a while before I've done any related rates problems, could someone please let me know if this is correct:

    Since, x and y must be changing at the same rate (presumably with respect to time) x' = y' and y' = -2xx'. Therefore, -2x = 1 and x = -1/2. Placing my x value into the original equation yields 15/4. Hence, the point is (-1/2, 15/4).

  2. jcsd
  3. SEEMS correct...
  4. Dick

    Dick 25,913
    Science Advisor
    Homework Helper

    Of course, it's right. What could go wrong?
  5. jgens

    jgens 1,621
    Gold Member

    Plenty, I could have made an incorrect assumption ultimately leading to false conclusions.
  6. quasar987

    quasar987 4,773
    Science Advisor
    Homework Helper
    Gold Member

    Good answer but you do not need to assume that x and y are varying wrt an external parameter. The derivative y'(x) = dy/dx of y wrt x expresses the instantaneous rate of change of y wrt a change in x.

    The points where y and x are changing at the same rate are those where y'(x)=1.
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