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Math Help - Double checking a related rates problem

  1. #1
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    Double checking a related rates problem

    Hey, I just wanted to see if anyone here has a moment to check that I didn't take any unreasonable steps in the solution to this problem:

    The point P moves so that at time t it is at the intersection of the curves
    x*y = t
    y = t*x^2

    How fast is the distance of P from the origin changing at t = 2?


    What I did was first to use the equation to eliminate t, which lead to x^3 = 1; i.e. P moves along x = 1. Then I substituted that back into the original equations, which in turn lead to y = t.
    Using the Pythagorean theorem I then calculated P's distance d from the origin as
    d^2 = 1 + y^2

    Calculating the derivative of this at t = y = 2 I got 2/sqrt(5)

    This is the correct answer according to the key; but I'm kinda green at this and I'm currently locked up at home with a cold, so basically I'd just be very grateful if anyone could check to see if the reasoning is correct!
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  2. #2
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    Lexington, MA (USA)
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    Re: Double checking a related rates problem

    Hello, Scurmicurv!

    Your reasoning and your work are correct.

    Good work!

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  3. #3
    Junior Member
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    Re: Double checking a related rates problem

    Thanks a lot, it's always a big help to have someone else confirm when you're just getting the hang of something!
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