- SUBJECT INDEX (Brief)

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z


- A -

absolute error, 339
absolute maxima and minima, 278, 283, 315
acceleration, 4, 323-324
accumulated change, 324, 404

approximating with left rectangles, 326-327, 337, 341
approximating with midpoint rectangles, 339, 348
approximating with right rectangles, 327-330, 337, 341
approximating with Simpson's Rule, 346
approximating with trapezoids, 338-339
difference of, 418, 466
errors in approximations, 339
estimating, 370-372
perpetual, 421, 424-425, 466

accumulation function, 361-362, 370, 387, 404-405

and area, 306, 404
derivative of, 379
for lines, 362-365, 377
formulas, 391-392
graphs, 365-368, 372-373
guidelines for sketching, 370

AIDS, 114, 132, 154, 190, 213-214, 463
algebraic method for slope, 208-209
aligning data, 44, 78
American Humane Association, 63-64
annual percentage rate, See APR
annual percentage yield, See APY
antiderivative, 379, 404-405

Exponential Rule, 384, 386
Constant Multiple Rule, 383, 386
Constant Rule, 382, 386
constant term, 394-395, 404
ex Rule, 384, 386
exception to Simple Power Rule, 384, 386
formulas, 381-383, 386, 397
general, 381-382, 387
notation, 381, 387, 405
Simple Power Rule, 382, 386
Sum Rule, 383, 386

approximating

accumulated change, 324-332
area, 404, 412-414
change, 302-305, 315-316
instantaneous rate of change, 173-174, 179, 199
with derivatives, 183-184, 199

APR, 93, 96-97, 135
APY, 93-94, 96, 135
area

as probability, 467-468
beneath a curve, 322-324, 351-352
between two curves, 412-414, 466
of circle, 339
of histogram, 465-466
of rectangles, 327, 329, 363
of triangle, 324
of trapezoid, 324, 338

arithmetic progressions, 42
AT&T Submarine Systems, 436
autoscaling, 119
average cost, 5
average rate of change, 144, 148-150, 179, 199, 455, 458, 467
average speed, 322-323
average value

of a function, 460, 467
of a quantity, 459, 467
of the rate of change, 456-458, 467

 
axes intercepts, 6, 47

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- B -

baby boomers, 344
best fit, 51-53, 80
biological stream, 432-434, 466
blood pressure, 361, 464
break-even point, 4, 6
bx rule for antiderivatives, 384, 386

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- C -

capital value, 437
Carbon 14, 425-426
Carson River, 340, 353, 396
Chain Rule for derivatives, 249-252, 269

Form 1, 250-254
Form 2, 252, 254

change

accumulated, 324, 394
and area, 324, 351-352, 412-414, 466
approximating, 302-305, 315-316
average rate of, 144, 148-150, 179, 199, 455
constant percentage, 74-76, 96
estimating instantaneous rate of, 173-174, 199
in a function, 304-305
in future value, 431
in present value, 432
instantaneous rate of, 156, 158-160, 170-174, 179, 185, 199, 268
percentage, 74-75, 191, 200
percentage rate of, 192, 200
rate of, 44, 66, 179, 199, 228, 268
results of, 324, 404

circle

slope, 164
tangent line, 163-165

Compaq Computer Corporation, 435
composition, 34-35, 251-252, 269
compound interest, 7, 22-23, 93-94, 135, 204
concave down/up, 80, 106, 121, 167
constant

graph, 9
multiplier, 383
percentage change, 74-76, 96

Constant Multiplier Rule for antiderivatives, 383-386
Constant Multiplier Rule for derivatives, 237, 239-240
Constant Multiplier Rule for limits, 423
Constant Rule for antiderivatives, 382-286
Constant Rule for derivatives, 239
Constant Rule for limits, 422
consumer price index, 52-53, 87, 130, 216, 248, 313
consumers'

expenditure, 286, 442-443, 467
surplus, 442-443, 450, 467
willingness and ability to spend, 439-441, 467

continuous, 20-25, 65, 282
curve/graph, 21, 65, 155-156, 172, 199, 210, 223

information, 21, 65, 155
model, 21
stream, 427

continuously compounded interest, 94-96, 135, 204, 428
costs

average, 5
fixed, 4, 5
start-up, 4, 5
total, 4, 5
variable, 4, 5

count data, 331, 356
CPI (consumer price index), 52-53, 87, 130, 216, 248, 313
Creative Technology, 435
critical point, 219
CSX-Conrail, 436
cubic

function/model, 100, 107-109, 123, 136
derivative, 230, 239

curve

continuous, 21, 65, 155, 172, 199, 210, 223
smooth, 155, 171, 210-211, 268

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- D -

data, 465

aligning, 44, 78
count, 331, 356

discrete, 21, 65, 155
distribution, 465

finding, 69, 319
linear, 43
reporting over time intervals, 147, 331
variability, 465

deceleration, 323-324
decreasing, 9
definite integral, 352, 387, 392, 405, 412

and area, 352-354, 387, 392
and area between two curves, 412-414, 466
as a limiting value of sums, 352, 387, 405, 412
evaluating, 392
interpretation, 353
of a piecewise continuous function, 395-398
sum property, 397
symbol, 352, 387, 405

demand curve, 438, 467
dependent variable, 17
depreciation, 47, 126
derivative, 179-180, 199, 228, 277, 315, 404

algebraic method, 208-209, 268
approximating with, 183-184, 199

Chain Rule, 249-252, 269
Constant Multiplier Rule, 239-240
Constant Rule, 239

existence of, 210, 223-224
financial market meaning, 190
formulas, 229-234, 239, 269
four-step method, 234
general formula, 234, 269
graph, 218, 277, 279-280, 282-283, 289
sketching, 218-222
interpreting, 181-182
limiting value definition, 234
Linear Function Rule, 239
notation, 268, 301
numerical method, 206-207, 268
of accumulation function, 379
of constant, 228, 239
of cubic function, 230, 239
of exponential function bx, 233, 236, 239
of exponential function ex, 230, 236, 239
of linear function, 227-229, 239
of natural log function, 239
of piecewise function, 210-211
of quadratic function, 229
Product Rule, 259, 269
second, 290-293, 315
Simple Power Rule, 231, 239
Sum Rule, 241-242, 269
units, 199, 380-381

diastolic blood pressure, 361, 464
differences

first, 49, 66, 74, 127
of accumulated changes, 418, 466
percentage, 74, 127
second, 101, 127
third, 107

diminishing returns, 275, 296
discount rate, 437
discrete, 20-25
data, 21, 155

graph, 21, 65
information, 21, 65, 155
income stream, 431-432

Disney, Walt, 86
domain, 17
Donner Memorial State Park, 14-15
doubling time, 188, 204

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- E -

e, 94-95
effective rate, 93
end behavior, 121, 123
equilibrium point, 449, 467
error

absolute, 339
deviation, 51
in approximating change, 339
round-off, 54-55
squared, 52

event, 467
ex Rule for antiderivatives, 384, 386
ex Rule for derivatives, 230, 236, 239
expected value

expenditure, 286, 442-443, 467
exponential
decay, 73
function/model, 73, 75-76, 93, 103, 135
growth, 73, 76
growth with constraints, 79

Exponential Rule for antiderivatives, 384, 386
Exponential Rule for limits, 423
extrapolation, 50
extreme point, 276, 280, 283, 315

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- F -

first differences, 49, 66, 74, 127
fixed costs, 4, 5
flow rate of income stream, 427-429, 466
function, 16, 20, 65

accumulation, 361-362, 370, 387, 404-405
adding, 32
average value of, 460, 467
combining, 32, 65-66
composition, 34-35, 66, 251-252, 269
continuous, 22, 65, 172
cubic, 100, 108, 123, 136, 695
demand, 438, 467
exponential, 73, 75-76, 93, 103, 135,
input, 17-19, 56, 65
inside, 35, 66, 252, 269
inverse, 30, 65
linear, 66, 121-123, 136
logistic, 79, 82, 95, 123, 135, 318
natural logarithm, 237, 239, 384
output, 17-18, 65,
outside, 35, 66, 251-252, 269
piecewise, 37, 66, 123, 171, 199, 210-211
polynomial, 100, 136
probability density, 468-470
product, 258
quadratic, 100, 104, 123, 136
rate of change, 218, 289, 324, 373
recovering, 380-381, 405
renewal, 433-434
subtracting, 32
supply, 445-448, 467
survival, 433-434

four-step analytic method, 234
Fundamental Theorem of Calculus, 321, 379, 390, 391, 404, 411
future value, 97, 135

of income stream, 427-428, 466
of biological stream, 434, 466

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- G -

Gateway Arch, 469-470
general antiderivative, 381-382, 387
geometric progression, 42, 72
Girl Scouts, 62
graph

constant, 9
continuous, 21, 65, 155, 172, 199, 210, 223
cosine, 527
decreasing, 9, 219
derivative, 218, 277, 279-280, 282-283, 289
discrete, 21, 65
histogram, 465-457
increasing, 9, 219
piecewise, 37, 66, 123, 171-172, 199, 282
rate of change, 218
sine, 505-507, 531
slope, 159, 179, 199, 218, 268, 277, 378-379
smooth, 155, 171, 210-211, 268
steepness of, 47, 49, 160, 220

Gross Domestic Product (GDP), 275, 288, 302
growth

exponential, 73, 76, 680
exponential with constraints, 79, 82
linear, 42-44
logistic, 79, 82

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- H -

half-life, 73
histogram, 465-467
horizontal limiting value, 79, 82, 95, 219
Houghton Mifflin Company, 46-47, 178

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- I -

improper integral, 421, 424-425, 466
income stream

continuous, 427, 466
discrete, 431-432, 466
future value, 427-428, 466
present value, 430, 466

increasing, 9
independent variable, 17
index

consumer price, 52-53, 87, 130, 216, 248, 313

inflection point, 80, 109, 121, 167, 169, 199, 218, 289, 294-296, 315
information

continuous, 21, 65, 155
discrete, 21, 65, 155

initial condition, 669, 673
input, 17-19, 56, 65
interval

input axis

between, 147
from...through, 147
from...to, 147

time, 331

input/output diagram, 17, 33, 66, 291
inside function, 35, 66, 251-252, 269, 604
instantaneous rate of change, 156, 158-160, 179, 268

and time, 185
estimating, 173-174, 199
existence of, 170-173, 210, 223-224

integral

definite, See definite integral
improper, 421, 424-425, 466
symbol, 352, 381, 387, 405

integration, 404-405
Intel, 88
intercept, 6, 47
interest

compound, 7, 22-23, 93-94, 135, 204
compounded continuously, 94-96, 135, 204, 428, 428

International Game Technology, 58
interpolation, 50
inverse function, 30, 65
inversely proportional, 671
irrational number, 95

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- J, K -

Jefferson National Expansion Memorial National Historic Site, 469
Kelly Services, 147-149, 194

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- L -

label, 56
Lake Tahoe, 151-152, 284-285, 298, 345-346
LCI International Telecommunications, 194
leading coefficient, 106
least squares method, 53
left rectangles, 326-327, 337, 341
leveling-off value, 79, 82, 219
limit

Constant Multiplier Rule, 423
Constant Rule, 422
definite integral, 412
Exponential Rule, 423
Negative Power Rule, 423
notation, 95, 421
of secant lines, 165-166, 206, 233-234, 268
of areas of midpoint rectangles, 348-352, 404
of sums, 348-352, 404
rules for evaluating, 422-424
Sum Rule, 423
with compound interest, 95, 135
with e, 95
with improper integral, 421, 466
with income streams, 428
with logistic model, 79, 82, 95, 120

line

best-fit, 51-53, 80
secant, 146, 148, 165-166, 199, 206, 208
slope of, 46, 66, 227-229, 234-236
tangent, 158, 163-168, 179, 199, 206-209, 304, 316

Linear Function Rule for derivatives, 239
linear function/model, 44-45, 47, 66, 69, 121-123, 136
local linearity, 169-170
logarithm function, 237, 239, 384
logistic

leveling-off/limiting value, 79, 82, 95, 219
function/model, 79, 82, 95, 123, 135, 318
slope graph, 219

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- M -

marginal

analysis, 275, 308, 316
cost, 308, 316, 385
profit, 308, 316
revenue, 308-309, 316

market equilibrium, 449, 467
market price, 441-445, 447, 467
mathematical model, 2, 65
mathematical modeling, 2-3, 8, 65
maximum

absolute, 278, 283, 315
local, See relative
relative, 276, 279, 283, 315

McDonnell Douglas, 333
mean, 473-474, 494
median, 473, 487
method of least squares, 53, 657, 661
midpoint rectangles, 339, 348
minimum

absolute, 278, 442, 283, 315
local, See relative
relative, 276, 279, 283, 315

model

best-fit, 51-53, 80
choosing, 119-128, 136
continuous, 21
cubic, 107-109, 120, 136
elements, 56
exponential, 73, 75-76, 93, 103, 135
label, 56
linear, 44-45, 47, 66, 69, 121-123, 136
logistic, 79, 82, 95, 123, 135, 318
mathematical, 2, 55
piecewise continuous, 37, 66, 123, 171, 199, 210
polynomial, 100, 136
quadratic, 101-103, 107, 136
reporting, 55
rounding, 55
use, 76
writing, 56

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- N -

National Rifle Association, 157, 160
natural log function, 237, 239, 384
Natural Log Rule for derivatives, 239
Negative Power Rule for limits, 423
nominal rate, 93, 135
normal distribution, 468
notation

derivative, 179-180, 199
integral, 352, 381, 387, 405

number sequences, 42
numerical method for slope, 206
numerical results

accuracy, 54-55, 57, 66
degree, 498-501
guidelines, 57, 66
irrational, 95
rounding, 54-55, 57, 66

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- O -

October Madness, 151
optimal point, See extreme point
optimization, 276-278, 280, 315
Ornda Healthcorp, 436
output, 17, 18, 65
outside function, 35, 66, 251-252, 269
overhead, 7

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- P -

parabola, 100-101, 136
PepsiCo, 435
percentage

change, 74-75, 191, 200, 680
differences, 101, 127
rate of change, 44, 66, 179, 199, 228, 268

perpetual accumulation, 421, 424-425, 466
piecewise continuous function, 37, 66, 123, 171, 199, 210-211
plot, See scatter plot
point

break even, 4, 6
critical, 218
equilibrium, 449, 467
extreme, 276, 280, 283, 315
of diminishing returns, 435, 459
of inflection, 80, 109, 121, 167, 169, 199, 218, 289, 294-296, 315
of least rapid change, 289
of most rapid change, 289
of tangency, 158
shutdown, 445

polio, 91
polynomial function/model, 100, 136
Power Rule, See Simple Power Rule
present value, 97-98, 135

of income stream, 430, 466

principal, 22
producers'

surplus, 447-448, 467
total revenue, 447-448, 467
willingness and ability to receive, 447-448, 467

product of functions, 258
Product Rule for derivatives, 259, 269
profit, 4, 5
progression

arithmetic, 42
geometric, 42, 72

PTA organization, 89, 154, 256
purchasing power of U. S. dollar, 41, 118, 195, 246, 266, 390

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- Q -

quadratic

function/model, 101-103, 107, 136
leading coefficient, 106

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- R -

range, 15
rate

annual percentage, 93
effective, 93
nominal, 93
of change, 44, 66, 179, 199, 228, 268
average, 144, 148-150, 179, 199, 455, 458, 467
average value of, 456-458, 467
estimating, 173-174
formulas, 229-234, 239
graph, 218
instantaneous, 156, 158-160, 170-174, 179, 185, 199, 210, 223-224
partial, 588-591, 593, 612
percentage, 192, 200

recovered function

input/output diagram, 380-381
units, 380-381

recovering a function, 380-381, 405
relative maximum, 276, 279, 283, 315
relative minimum, 276, 279, 283, 315
renewal function, 433-434
Reno Air, 58
results of change, 324, 404
revenue, 4, 5, 258, 286

continuous rate of flow, 360
total, 447-448, 467

right rectangles, 327-330, 337, 341
rise, 48
rounding, 54-55, 57, 66
Rule of 72, 204
run, 47
Russell Corporation, 300-301

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- S -

scatter plot, 21, 65, 119-121, 222
Sears, 436
secant

line, 146, 148, 165-166, 199, 206, 208
slope, 146, 148, 199, 233-234
of an angle, B2

second derivative, 290-293, 315

units, 290

second differences, 101, 127
shutdown point, 445
Simple Power Rule for antiderivatives, 382, 386
Simple Power Rule for derivatives, 231, 239
Simpsonís Rule, 346
slope

algebraic method, 208-209
formulas, 227-234, 239, 269
graph, 159, 179, 199, 218-223, 268
of curve, 158, 164, 179, 199
of graph, 159, 179
of line, 46-48, 66, 227-229, 234-236
of piecewise function, 210-211
of secant line, 146, 148, 199, 233-234
of tangent line, 158, 172, 179, 199, 206-210, 268
trend, 207-208
undefined, 171-172, 223-224

social gain, 449-450, 467
speed, See velocity
SSE, 75
St. Louis Arch, 469-470
start-up costs, 4, 5
stationary point, See critical point
steepness, 47, 49, 160, 220
stream

biological, 432-434, 466
income, 427, 431-432, 466

Sum Rule for antiderivatives, 383, 386
Sum Rule for derivatives, 240-241, 269
Sum Rule for limits, 423
supply curve, 445-448, 467
surplus

consumers', 442-443, 450, 467
producers', 447-448, 467

survival function, 433-434
symmetric difference quotient, 173-174, 179

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- T -

tangent

line, 158, 163-168, 179, 199, 206, 304, 316
algebraic method for slope, 208-209, 268
approximating with, 673
construction, 163-164
horizontal, 315
numerical method for slope, 206-207, 268
on a circle, 163, 165
point, 158
slope as a limiting value, 206, 268
slope, 158-160, 167, 172, 199, 223-224, 236, 268
vertical, 224, 268

technology, 66
Tenet Healthcare Corporation, 436
third difference, 107
tilt, See slope
total cost, 4, 5
total revenue, 447-448
total social gain, 449-450, 467
Toys R Us, 193-194
trapezoid approximation, 338-339
trend, 348-349

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- U -

units

labeling, 56

Uranium 238, 427 

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- V -

variable

controlled, 17
costs, 4
dependent, 17
independent, 17
labeling, 56
observed, 17
random, 467

variable costs, 4, 5
velocity, 322-324
Vertical Line Test, 20, 65
Visa cards, 197

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- W -

Washington Monument, 389
willingness and ability to receive, 447-448, 467
willingness and ability to spend, 441, 467
Winnemucca and Esmeralda silver lodes, 455





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