Exam 3: Differentiation

Suppose measures an economy's personal consumption expenditure and x the personal income, both in billions of dollars. Then, measures the economy's savings corresponding to an income of x billion dollars. Then . ​ The quantity dS/dx is called the marginal propensity to save. ​ For the consumption function , where and x are measured in billions of dollars, find the marginal propensity to save when . ​

Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the equation . ​ If 25,000 cartons of eggs are available at the beginning of a certain week and the supply is falling at the rate of 1,000 cartons/week, at what rate is the wholesale price changing? (Hint: To find the value of p when, solve the supply equation for p when).

If the marginal profit function is positive at , then it makes sense to increase the level of production.

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

Find the derivative of the function. ​ ​

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , . ​

Find the derivative of the function. ​

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

Find the given limit by evaluating the derivative of a suitable function at an appropriate point. ​ ​

The distance s (in feet) covered by a car after t sec is given by . Find a general expression for the car's acceleration at any time .

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. ​ ​

Find the differential of the function. ​ ​

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. Compute . Round your answer to the nearest thousandth. __________% per year in the second power

Find the derivative of the function. ​ ​ ​

If f is differentiable, then .

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

In a test flight of the McCord Terrier, McCord Aviation's experimental VTOL (vertical takeoff and landing) aircraft, it was determined that t sec after liftoff, when the craft was operated in the vertical takeoff mode, its altitude (in feet) was ​ . Find an expression for the craft's acceleration at time t.

Find the differential of the function.

Find the differential of the function.