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Point on a Curve 
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#1
Jan2009, 10:27 PM

P: 1,622

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). Thanks. 


#2
Jan2009, 10:37 PM

P: 36

SEEMS correct...



#3
Jan2009, 11:08 PM

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Thanks
P: 25,251

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



#4
Jan2009, 11:13 PM

P: 1,622

Point on a Curve
Plenty, I could have made an incorrect assumption ultimately leading to false conclusions.



#5
Jan2009, 11:15 PM

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P: 4,772

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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