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stability of inverse proportional realtion for large numbers

What I figured out is,
   The function with variables x and y and a konstant k provided such that xy=k has strong stabilty in y when x is very large.
i.e. a bit of change in x (for large x values) is not going to disturb the value of y as much as x does.
  for xy=k
D(xy)=0  =>  xDy+yDx=0
 ===> Dy=-k/sqr(x) * Dx
  for larger values of x  the change Dx is vanishes to Dy.

P.S: same can be applied for y variable though.

1 వ్యాఖ్య:

రౌతు విజయకృష్ణ చెప్పారు...

Take x to be the amount of food in the world and y to be the price of all the food And k as the Food constant (requirement) of All the world People. This example is one of the easily understandable case.