• A •
absolute maximum and minimum, 66–67,
290–293
absolute value equations, 11, 142–143
absolute value inequalities, 12, 150
acceleration, 85–86, 382–386
adding polynomials, 14, 159
algebra
absolute value equations, 11, 142–143
absolute value inequalities, 12, 150
adding polynomials, 14, 159
domain and range of a function and its inverse,
10, 137–138
end behavior of polynomials, 14, 158–159
finding domain and range from graphs, 13–14,
157–158
graphing common functions, 12–13, 150–157
horizontal line test, 9, 133–134
linear equations, 10, 138–139
long division of polynomials, 15, 162–163
multiplying polynomials, 15, 161
polynomial inequalities, 12, 145–149
problem types, 7
quadratic equations, 10–11, 139–141
rational inequalities, 12, 145–149
simplifying
fractions, 8, 127–131
radicals, 8–9, 131–133
solving
polynomial equations by factoring, 11,
141–142
rational equations, 11, 144–145
subtracting polynomials, 14–15, 160
tips for, 7
amplitude, 23, 177
angles, finding in coordinate plane, 19–20, 168
answers to practice problems. See specific topics
antiderivatives. See also Riemann sums
examples of, 81–84, 365–375
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions, 101,
475–481
applications of derivatives
applying Rolle’s theorem, 69, 311–313
approximating roots using Newton’s method,
73, 335–338
closed interval method for finding maximum
and minimum, 67, 291–293
determining concavity, 68–69, 300–303
estimating values with linearizations, 64,
233–234, 236–237, 279–283
evaluating differentials, 64, 278
finding
absolute maximum and minimum with closed
intervals, 67, 291–293
intervals of increase and decrease, 68,
293–296
local maxima and minima using first
derivative test, 68, 296–300
local maxima and minima using second
derivative test, 69, 307–311
maxima and minima from graphs, 66–67,
290–291
speed, 70–71, 318–321
velocity, 70–71, 318–321
identifying inflection points, 69, 303–307
optimization problems, 71–72, 321–335
problem types, 63
related rates, 64–66, 283–290
relating velocity and position, 70,
316–318
solving problems with mean value theorem,
70, 313–316
tips for, 63
approximating roots using Newton’s method,
73, 335–338
area. See Riemann sums
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
• C •
Calculus For Dummies (Ryan), 3
Calculus II For Dummies (Zegarelli), 3
chain rule, 49, 52–54, 248–256
Cheat Sheet (website), 2
classifying discontinuities, 38–40,
218–221
closed interval method, 67, 291–293
coefficients, 117–118, 557–560
comparison test, 123, 589–591
concavity, 68–69, 300–303
continuity, 39–40, 219–224
Index
absolute maximum and minimum, 66–67,
290–293
absolute value equations, 11, 142–143
absolute value inequalities, 12, 150
acceleration, 85–86, 382–386
adding polynomials, 14, 159
algebra
absolute value equations, 11, 142–143
absolute value inequalities, 12, 150
adding polynomials, 14, 159
domain and range of a function and its inverse,
10, 137–138
end behavior of polynomials, 14, 158–159
finding domain and range from graphs, 13–14,
157–158
graphing common functions, 12–13, 150–157
horizontal line test, 9, 133–134
linear equations, 10, 138–139
long division of polynomials, 15, 162–163
multiplying polynomials, 15, 161
polynomial inequalities, 12, 145–149
problem types, 7
quadratic equations, 10–11, 139–141
rational inequalities, 12, 145–149
simplifying
fractions, 8, 127–131
radicals, 8–9, 131–133
solving
polynomial equations by factoring, 11,
141–142
rational equations, 11, 144–145
subtracting polynomials, 14–15, 160
tips for, 7
amplitude, 23, 177
angles, finding in coordinate plane, 19–20, 168
answers to practice problems. See specific topics
antiderivatives. See also Riemann sums
examples of, 81–84, 365–375
of hyperbolic functions, 102–103, 485–489
involving inverse trigonometric functions, 101,
475–481
applications of derivatives
applying Rolle’s theorem, 69, 311–313
approximating roots using Newton’s method,
73, 335–338
closed interval method for finding maximum
and minimum, 67, 291–293
determining concavity, 68–69, 300–303
estimating values with linearizations, 64,
233–234, 236–237, 279–283
evaluating differentials, 64, 278
finding
absolute maximum and minimum with closed
intervals, 67, 291–293
intervals of increase and decrease, 68,
293–296
local maxima and minima using first
derivative test, 68, 296–300
local maxima and minima using second
derivative test, 69, 307–311
maxima and minima from graphs, 66–67,
290–291
speed, 70–71, 318–321
velocity, 70–71, 318–321
identifying inflection points, 69, 303–307
optimization problems, 71–72, 321–335
problem types, 63
related rates, 64–66, 283–290
relating velocity and position, 70,
316–318
solving problems with mean value theorem,
70, 313–316
tips for, 63
approximating roots using Newton’s method,
73, 335–338
area. See Riemann sums
area between curves, 88–89, 387–406
average value of functions, 97–98, 463–470
• C •
Calculus For Dummies (Ryan), 3
Calculus II For Dummies (Zegarelli), 3
chain rule, 49, 52–54, 248–256
Cheat Sheet (website), 2
classifying discontinuities, 38–40,
218–221
closed interval method, 67, 291–293
coefficients, 117–118, 557–560
comparison test, 123, 589–591
concavity, 68–69, 300–303
continuity, 39–40, 219–224
Index