Question

A price p (in dollars) and demand x for a product are related by 2x 2 +4xp+50p 2 =6600 If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand. Rate of change of demand =

Answer 1

To find the rate of change of the demand, differentiate the given equation with respect to time and solve for dx/dt.

Step-by-step explanation:

To find the rate of change of the demand, we need to differentiate the given equation with respect to time. Let's differentiate the equation:

4x(dx/dt) + 4p + 4xdp/dt + 100p(dp/dt) = 0

Now, we can substitute the given values to solve for dx/dt:

4(10)(dx/dt) + 4(10) + 4(10)(2) + 100(10)(dp/dt) = 0

(40 + 40 + 80)dx/dt + 1000(dp/dt) = 0

160dx/dt + 1000(dp/dt) = 0

160dx/dt = -1000(dp/dt)

dx/dt = -6.25(dp/dt)

Therefore, the rate of change of the demand is -6.25 times the rate of change of the price.