Rate of change - Implicit differentiation
"A price p (in dollars) and demand x for a product are related by
(2x^2)-2xp+50p^2 = 20600.
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand."
I was a little confused on how to proceed with this question. Am I supposed to use implicit differentiation (with the x serving the same purpose as a y) and then find the derivative of x?
This is the implicit differentiation I tried:
4x(dx/dp)-2(dx/dp)+100p = 0
4x(dx/dp)-2(dx/dp) = -100p
dx/dp(4x-2) = -100p
dx/dp = -100p/4x-2
I believe this is the derivative I am looking for (though not entirely sure) but I am not sure what values of p and x to input, as I am supposed to get a numerical final answer.
Any help?
"A price p (in dollars) and demand x for a product are related by
(2x^2)-2xp+50p^2 = 20600.
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand."
I was a little confused on how to proceed with this question. Am I supposed to use implicit differentiation (with the x serving the same purpose as a y) and then find the derivative of x?
This is the implicit differentiation I tried:
4x(dx/dp)-2(dx/dp)+100p = 0
4x(dx/dp)-2(dx/dp) = -100p
dx/dp(4x-2) = -100p
dx/dp = -100p/4x-2
I believe this is the derivative I am looking for (though not entirely sure) but I am not sure what values of p and x to input, as I am supposed to get a numerical final answer.
Any help?
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