Exam 3: Differentiation

The demand equation for the Sicard wristwatch is given by , where x (measured in units of a thousand) is the quantity demanded each week and p is the unit price in dollars.Find the rate of change of the quantity demanded of the wristwatches with respect to the unit price when the unit price is $60.Round your answer to the nearest whole number.

Find the third derivative of the function.

The demand equation for the Sicard wristwatch is given by where x (measured in units of a thousand) is the quantity demanded each week and p is the unit price in dollars.Find the rate of change of the quantity demanded of the wristwatches with respect to the unit price when the unit price is $35.Round your answer to the nearest whole number. __________ wristwatches/(dollar price increase)

The demand function for a certain brand of compact disc is , where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Compute the elasticity of demand (to the nearest hundredth) when x = 10. __________ Determine whether the demand is inelastic, unitary, or elastic when x = 10. __________

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

Suppose f and g are functions that are differentiable at and that , , , and .Find the value of .

Use a differential to approximate the quantity to the nearest thousandth.

Find the derivative of the function.

Find the differential of the function.

Find the derivative of the function.

Find by implicit differentiation.

Find the first and second derivatives of the function.

Find by implicit differentiation.

Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is where k is a constant.Suppose a dose of the drug TPA increases r by 22%.How will this affect the resistance R? Assume that l is constant.

Suppose f and g are functions that are differentiable at and that , , , and .Find the value of .

Find the slope m and an equation of the tangent line to the graph of the function f at the point .

The supply equation for a certain brand of radio is given by , where x is the quantity supplied and p is the unit price in dollars.Use differentials to approximate the change in price when the quantity supplied is increased from 10,000 units to 10,500 units. $__________

The percent of mothers who work outside the home and have children younger than age 6 yr is approximated by the function where t is measured in years, with t = 0 corresponding to the beginning of 1980. Compute .

A hemisphere-shaped dome of radius 30 ft is to be coated with a layer of rust-proofer before painting.Use differentials to estimate the amount of rust-proofer needed if the coat is to be 0.05 in.thick. Hint: The volume of a hemisphere of radius r is .

Let .Find .