A price p (in dollars) and demand x for a product are related by
2x^2+1xp+50p^2=26000.
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.
Rate of change of demand =
1
Expert's answer
2012-10-30T10:02:08-0400
p=20 so 2x^2+x*20+50*20^2=26000 x=-60 or x=50 but x>0 so x=50 x, p functions of time t and we know that dp/dt=2 at point x=50 p=20 we must find dx/dt differentiate equation 4xdx+x*dp+p*dx+100*p*dp=0 (: dt) 4x*dx/dt +x*dp/dt+100*p*dp/dt=0 for dx/dt we have 4*50*dx/dt+50*2+100*20*2=0 2*dx/dt+1+20*2=0 dx/dt=-41/2 rate of change of the demand=-41/2
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