Business Calc Question!!!!

Question

Suppose the quantity demanded weekly of Super Titan radial tires is related to its unit price by the equation, p+x^2 =144 where p is unit price measured in dollars and x is measured in units of a thousand. How fast is the quantity demanded weekly changing when the unit price per tire is 63 and the price per tire is increasing at a rate of $2 per week? Is it increasing or decreasin?

Answer 1

Since you know the unit price, you can find the demand quantity by substituting p=63 and solving for x.

 

You're then looking for the rate of change of the quantity, which means a derivative. Taking the implicit derivative with respect to t, you get

dp/dt + d (x^2) / dt = 0

dp/dt + 2x dx/dt = 0

 

dp/dt is given in the problem, and you solved for x earlier, so you can now solve this for dx/dt.