Exam 3: Differentiation

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 68 to 76 items. Round to the nearest second.

The base of a 25-ft ladder leaning against a wall begins to slide away from the wall. At the instant of time when the base is 24 ft from the wall, the base is moving at the rate of 7 ft/sec. How fast is the top of the ladder sliding down the wall at that instant of time? Round the answer to the nearest tenth, if necessary. __________ ft/sec

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule , where N(t) denotes the population at the end of year t. Find the rate of growth of the turtle population when .

In calm waters oil spilling from the ruptured hull of a grounded tanker spreads in all directions. If the area polluted is a circle and its radius is increasing at a rate of 3 ft/sec, determine how fast the area is increasing when the radius of the circle is 30 ft.

The quantity demanded each week x (in units of a hundred) of the Mikado miniature camera is related to the unit price p (in dollars) by the demand equation . When is demand unitary? Hint: Solve for p.

Determine whether the statement below is true or false. If the marginal profit function is negative at , then it makes sense to increase the level of production.

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 72 to 78 items. Round to the nearest second. __________ sec

Find the third derivative of the function.

Find the derivative of the function.

Find the derivative by solving the given implicit equation for y explicitly in terms of x.

Find the derivative by solving the given implicit equation for y explicitly in terms of x.

Find by implicit differentiation.

The consumption function of the U.S. economy from 1929 to 1941 is , where is the personal consumption expenditure and is the personal income, both measured in billions of dollars. Find the rate of change of consumption with respect to income, . This quantity is called the marginal propensity to consume. Round the answer to three decimal places, if necessary. __________

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is dollars/year. Find the average cost function C.

A 5-ft tall man is walking away from a street light 10 ft high at a speed of 5 ft/sec. How fast is the tip of his shadow moving along the ground?

Find the first and second derivatives 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 t = 0 corresponding to the beginning of 1980. Compute . Round your answer to the nearest thousandth. __________% per year in the second power

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule , where denotes the population at the end of year t. Find the rate of growth of the turtle population when . __________ turtles/yr Find the rate of growth of the turtle population when . __________ turtles/yr What will be the population 10 yr after the conservation measures are implemented? __________ turtles