Multiple Choice Identify the
choice that best completes the statement or answers the question.


1.

Find the slope of the tangent line to the graph of each function at the given
point and determine an equation of the tangent line.


2.

Let Find the equation of the tangent line to
the curve at the point .


3.

Let . Find the derivative of
and the point on the graph of where the tangent line to the
curve is horizontal.


4.

During the construction of a highrise building, a worker accidentally dropped
his portable electric screwdriver from a height of 144 ft. After t sec, the screwdriver had
fallen a distance of ft. What was the velocity of the
screwdriver at the time it hit the ground?
a.  48 ft/sec  b.  12 ft/sec  c.  96
ft/sec  d.  768 ft/sec 


5.

Under a set of controlled laboratory conditions, the size of the population of a
certain bacteria culture at time t (in minutes) is described by the function Find the rate of population growth at min.
a.  125 bacteria per minute  b.  148 bacteria per minute  c.  120 bacteria per
minute  d.  113 bacteria per minute 


6.

The position of car A and car B, starting out side by side and traveling along a
straight road, is given by and , respectively, where s
is measured in feet and t is measured in seconds (see the accompanying figure). Which car is traveling faster at ?


7.

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 .
a.  26 turtles/yr  b.  32 turtles/yr  c.  28
turtles/yr  d.  30 turtles/yr  e.  24 turtles/yr 


8.

Let . Find the values of x for which
.


9.

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


10.

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


11.

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


12.

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


13.

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


14.

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


15.

Let . Find .


16.

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


17.

Retail revenue each year from Internet shopping is approximated by the function
, where is measured in billions of
dollars and t is measured in years, with corresponding to the beginning
of 1997. How fast was the retail revenue/year from Internet shopping changing at the
beginning of the year 2000?


18.

Find the derivative of the function.


19.

Find the derivative of the function.


20.

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


21.

Evaluate at the value of .


22.

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


23.

Find the derivative of the function.


24.

Find the derivative of the function.


25.

Find the derivative of the function.


26.

The number of viewers of a television series introduced several years ago is
approximated by the function , where N(t) (measured in millions) denotes
the number of weekly viewers of the series in the t^{ th} week. Find the rate
of increase of the weekly audience at the end of week 12.
a.  0.165 million/wk  b.  2.694 million/wk  c.  0.495
million/wk  d.  8.082 million/wk  e.  16.332
million/wk 


27.

Suppose . Find given that , , , .


28.

Find the derivative of the function.


29.

Find the derivative of the function.


30.

Find the derivative of the function.


31.

Find the derivative of the function.


32.

A division of Ditton Industries manufactures the Futura model microwave oven.
The daily cost (in dollars) of producing these microwave ovens is where
x stands for the number of units produced. What is the actual cost incurred in manufacturing
the 301 ^{st} oven and the marginal cost when ?
a.  The actual cost of the 301^{st} oven is $138.12, the marginal cost when is $138.00  b.  The actual cost of the 301^{st} oven is
$118.12, the marginal cost when is $36.00  c.  The actual cost of
the 301^{st} oven is $118.12, the marginal cost when is
$120.00  d.  The actual cost of the 301^{st} oven is $18.12, the marginal cost when
is $156.00  e.  The actual cost of the 301^{st} oven is
$138.12, the marginal cost when is $156.00 


33.

Pulsar manufactures a series of 19in. 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 , ,
.
a.  , ,  b.  , ,  c.  , ,  d.  , ,  e.  , , 


34.

The total weekly cost (in dollars) incurred by a company in pressing x
compact discs is . What is the marginal cost when and ?


35.

The management of Acrosonic plans to market the ElectroStat, an electrostatic
speaker system. The marketing department has determined that the demand for these speakers is , where p denotes the speaker's unit price (in dollars) and x denotes
the quantity demanded. Find the marginal revenue function .


36.

Find the second derivative of the function.


37.

Find the second derivative of the function.


38.

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 t.


39.

Find the first and second derivatives of the function.


40.

Find the first and second derivatives of the function.


41.

Find the first and second derivatives of the function.


42.

Find the first and second derivatives of the function.


43.

During the construction of an office building, a hammer is accidentally dropped
from a height of 256 ft. The distance the hammer falls in t sec is . What is the
hammer's velocity when it strikes the ground? What is its acceleration?

Numeric Response


44.

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

Short Answer


45.

Let Find the derivative of
. __________ Find the equation of the
tangent line to the curve at the point . __________ Select the correct
graph of by answering A, B, or C.
__________


46.

Let . Find the derivative of
. __________ Find the point on the graph of
f where the tangent line to the curve is horizontal. __________ Sketch the
graph of f and the tangent line to the curve at the point where the tangent line to the curve
is horizontal. Select the correct graph by entering A, B, or C.
__________ Let represent the point on the graph of f
where the tangent line to the curve is horizontal. What is the rate of change of f at this
point? __________


47.

Find the derivative of the function.


48.

Find the derivative of the function.


49.

Find the derivative of the function.


50.

Find the derivative of the function.


51.

Find the derivative of the function.


52.

Find .


53.

Find the first and second derivatives of the function.


54.

Find the third derivative of the function.
