Exam 3: Differentiation

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. When is the demand unitary? (Hint: Solve for p).

Find the derivative of the function by using the rules of differentiation.

Find by implicit differentiation.

Find the differential of the function.

Find the differential of the function.

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. Is the demand elastic or inelastic when ? __________ Is the demand elastic or inelastic when __________ When is the demand unitary? Round the answer to two decimal places. (Hint: Solve for p). __________ If the unit price is increased slightly from $10, will the revenue increase or decrease? __________ If the unit price is lowered slightly from $8, will the revenue increase or decrease? __________

Find the derivative of the function.

Let . Find the point(s) on the graph of f where the tangent line is horizontal.

The quantity of Sicard wristwatches demanded each month is related to the unit price by the equation , where p is measured in dollars and x in units of a thousand. Find the marginal revenue function .

Find the derivative of the function f by using the rules of differentiation.

The proprietor of the Showplace, a video store, has estimated that the rental price p (in dollars) of prerecorded video discs is related to the quantity x rented/day by the demand equation . Currently, the rental price is $5/disc. Is the demand elastic or inelastic at this rental price? __________ If the rental price is increased, will the revenue increase or decrease? __________

Find the derivative of the function.

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 .

Find the derivative of the function by using the rules of differentiation.

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 corresponding to the beginning of 1980. At what rate was the percent of these mothers changing at the beginning of 2001?

The demand equation is . Compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at .

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function.

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.