Related Rates 

1. Suppose \( x^2+4y^2=17\), where \(x\)  and \(y\)  are functions of \(t\).  Find  \(\frac{dy}{dt}\) if given that \(\frac{dx}{dt}= 1.5\), \(x=3\) and \(y=2\).  solution

 2. Suppose the quantity demanded weekly of the SuperTitan radial tire is related to its unit price by the equation \(p + x^2 = 144\) where \(p\) is measured in dollars and \(x\) is measured in units of 1000. How fast is the quantity demanded weekly changing when \(x=8, p = \$80\) and the price per tire is increasing at a rate of $4 per week?  solution

3. The demand equation for a certain brand of earbuds is \(100x^2 + 8p^2 = 2358\) where \(x\) represents the number (in thousands) of earbuds demanded each week that the unit price is $p. How is the quantity demanded changing when the unit price per set of earbuds is $13.50 and the price is dropping at a rate of $0.12 per earbud set per week?  solution