INDEX Q 447
Exponential growth and decay
(Cont.):
radioactive decay, 26.15 to
26.18, 26.21, 26.30, 26.43
rate of increase for, 26.4
Extrema (maxima and minima) of
functions:
absolute:
critical numbers and, 13.9 to
13.13, 13.15 to 13.17,
13.21, 13.23 to 13.34,
13.36, 15.31
of exponential functions, 24.50,
24.57 to 24.62, 24.73
of multivariate functions,
43.54, 43.55, 43.65
applications of, 16.1 to 16.61
Lagrange multipliers and, 43.56
to 43.64, 43.66, 43.67
relative:
critical numbers and, 13.3 to
13.8, 13.14, 13.18 to 13.20,
15.6 to 15.15, 15.17 to
15.22, 15.31 to 15.35,
15.39, 15.41 to 15.46, 15.48
to 15.51, 15.53, 15.54
first derivative test for, 13.2,
13.6 to 13.8, 13.18, 13.20,
13.29,15.10,15.11,15.14,
15.15, 15.19,15.34,15.37,
15.44, 15.45, 15.49
inflection points and, 13.2,
13.6, 13.7, 13.18, 13.20,
14.42 to 14.46, 15.7, 15.8,
15.10 to 15.19, 15.32 to
15.35, 15.48 to 15.51,
15.57, 15.61
of multivariate functions, 43.22
to 43.53
second derivative test for, 13.1,
13.3 to 13.7, 13.20, 13.21,
15.1 to 15.9, 15.12, 15.13,
15.16to 15.18, 15.20 to
15.29, 15.32, 15.33, 15.35,
15.37, 15.39 to 15.56
Factorization of polynomials, 5.76
to 5.86
Fahrenheit temperature scale, 3.71
First derivative test for relative
extrema, 13.2, 13.6 to 13.8,
13.18, 13.20, 13.29, 15.10,
15.11, 15.14, 15.15, 15.19,
15.34, 15.37, 15.44, 15.45,
15.49
(See also Second derivative test
for relative extrema)
Frequency of trigonometric
functions, 10.12
Frustrum of cones, 22.49
Functions:
asymptotes of, 6.28 to 6.32,
15.17to 15.19, 15.26, 15.39
to 15.43, 15.47, 15.48, 15.50,
15.52, 15.58, 15.59, 15.61
average value of, 20.32, 20.33,
20.40, 20.57, 20.91
composite, 9.1 to 9.6, 9.24 to
9.34, 9.46, 10.19
concave, 15.1 to 15.5, 15.16,
15.17, 15.20, 15.21, 15.23 to
15.29, 15.39 to 15.41, 15.43,
15.44, 15.48, 15.52, 34.29,
34.30
continuity of (see Continuity of
functions)
contour maps (level curves) of,
41.32 to 41.43
critical numbers of (see Critical
numbers)
decreasing, 11.19 to 11.26
derivatives of (see Derivatives)
differentiable, 8.21, 8.25, 8.26,
8.30, 8.31,8.43 to 8.47,
9.18,9.45,9.49
discontinuities in (see Continuity
of functions)
domain of, 5.1 to 5.19, 5.24 to
5.31, 5.34 to 5.37, 9.16,
27.21, 41.64 to 41.66
even, 5.38, 5.40, 5.41,5.48, 5.53,
5.55,5.56,5.90,5.91,5.93,
8.46, 8.47, 15.31, 15.36,
15.46, 20.50, 38.73, 38.93
exponential (see Exponential
functions)
extrema of (see Extrema of
functions)
gamma, 32.22
greatest integer, 5.6, 5.7, 6.5
homogeneous multivariate, 42.74
to 42.80
hyperbolic (see Hyperbolic
functions)
increasing, 11.18, 11.20 to 11.26,
11.29, 11.48, 15.52
inflection points of, 13.2, 13.6,
13.7, 13.18, 13.20, 15.2,
15.3, 15.5, 15.7, 15.8, 15.10
to 15.19, 15.21, 15.25, 15.26,
15.32 to 15.35, 15.37, 15.40,
15.42 to 15.46, 15.48 to
15.51, 15.53, 15.57, 15.61
integrals of (see Integrals)
inverse, 5.69 to 5.74, 5.92, 5.93,
5.100,9.49
level surfaces of, 41.44 to 41.47
limits of (see Limits)
logarithmic (see Natural
logarithms)
Functions (Cont.):
maxima and minima of (see
Extrema of functions)
multivariate, 41.1 to 41.66
odd, 5.43, 5.44, 5.46, 5.49, 5.51,
5.52, 5.54 to 5.56, 5.90 to
5.92, 8.46, 8.47, 15.34,
15.47, 15.51, 20.48, 20.49,
24.97, 38.74, 38.93
one-one, 5.57, 5.58, 5.60, 5.63,
5.69 to 5.74, 5.92, 5.93,
5.100, 9.49
polynomial (see Polynomials)
range of, 5.1 to 5.19, 5.24 to
5.31, 5.34 to 5.37, 27.21
rational, integration of, 30.1 to
30.33
self-inverse, 5.69, 5.74, 5.75
of several variables, 41.1 to
41.66
strictly increasing, 11.48
strictly positive, 11.48
trigonometric (see Trigonometric
functions)
Fundamental theorem of calculus,
20.9 to 20.14
Gamma function, 32.22
Gauss' theorem, 45.49
Generalized mean value theorem,
11.38, 11.39
Geometric mean, 43.51
Geometric series, 37.5 to 37.9,
37.12, 37.13, 37.25, 37.26,
37.30 to 37.34, 37.45, 37.48,
37.67, 37.68, 37.73, 37.75,
37.77,37.83,37.91,37.113
to 37.116, 38.5, 38.26, 38.29
Gradient, 43.1 to 43.22, 43.56 to
43.64, 43.66, 43.67, 45.24,
45.32, 45.33, 45.35, 45.36,
45.39, 45.45
Graphs:
absolute extrema in, 15.31, 15.61
asymptotes in, 6.28 to 6.32,
15.17 to 15.19, 15.26, 15.39
to 15.43, 15.47, 15.48, 15.50,
15.52, 15.58, 15.59, 15.61
cardioids, 35.30, 35.34 to 35.36,
35.44, 35.66, 35.67, 35.69,
44.33, 44.38, 44.81
circles, 5.3, 34.1, 35.7 to 35.9,
35.13, 35.14, 35.17, 35.18,
35.41, 35.66, 35.67, 35.69,
35.87, 44.33, 44.37, 44.38,
44.42, 44.44
cones, 41.8, 41.10, 41.16
cubic functions, 5.10, 5.19, 41.34
cusps in, 15.44
cylinders, 41.1, 41.2
Exponential growth and decay
(Cont.):
radioactive decay, 26.15 to
26.18, 26.21, 26.30, 26.43
rate of increase for, 26.4
Extrema (maxima and minima) of
functions:
absolute:
critical numbers and, 13.9 to
13.13, 13.15 to 13.17,
13.21, 13.23 to 13.34,
13.36, 15.31
of exponential functions, 24.50,
24.57 to 24.62, 24.73
of multivariate functions,
43.54, 43.55, 43.65
applications of, 16.1 to 16.61
Lagrange multipliers and, 43.56
to 43.64, 43.66, 43.67
relative:
critical numbers and, 13.3 to
13.8, 13.14, 13.18 to 13.20,
15.6 to 15.15, 15.17 to
15.22, 15.31 to 15.35,
15.39, 15.41 to 15.46, 15.48
to 15.51, 15.53, 15.54
first derivative test for, 13.2,
13.6 to 13.8, 13.18, 13.20,
13.29,15.10,15.11,15.14,
15.15, 15.19,15.34,15.37,
15.44, 15.45, 15.49
inflection points and, 13.2,
13.6, 13.7, 13.18, 13.20,
14.42 to 14.46, 15.7, 15.8,
15.10 to 15.19, 15.32 to
15.35, 15.48 to 15.51,
15.57, 15.61
of multivariate functions, 43.22
to 43.53
second derivative test for, 13.1,
13.3 to 13.7, 13.20, 13.21,
15.1 to 15.9, 15.12, 15.13,
15.16to 15.18, 15.20 to
15.29, 15.32, 15.33, 15.35,
15.37, 15.39 to 15.56
Factorization of polynomials, 5.76
to 5.86
Fahrenheit temperature scale, 3.71
First derivative test for relative
extrema, 13.2, 13.6 to 13.8,
13.18, 13.20, 13.29, 15.10,
15.11, 15.14, 15.15, 15.19,
15.34, 15.37, 15.44, 15.45,
15.49
(See also Second derivative test
for relative extrema)
Frequency of trigonometric
functions, 10.12
Frustrum of cones, 22.49
Functions:
asymptotes of, 6.28 to 6.32,
15.17to 15.19, 15.26, 15.39
to 15.43, 15.47, 15.48, 15.50,
15.52, 15.58, 15.59, 15.61
average value of, 20.32, 20.33,
20.40, 20.57, 20.91
composite, 9.1 to 9.6, 9.24 to
9.34, 9.46, 10.19
concave, 15.1 to 15.5, 15.16,
15.17, 15.20, 15.21, 15.23 to
15.29, 15.39 to 15.41, 15.43,
15.44, 15.48, 15.52, 34.29,
34.30
continuity of (see Continuity of
functions)
contour maps (level curves) of,
41.32 to 41.43
critical numbers of (see Critical
numbers)
decreasing, 11.19 to 11.26
derivatives of (see Derivatives)
differentiable, 8.21, 8.25, 8.26,
8.30, 8.31,8.43 to 8.47,
9.18,9.45,9.49
discontinuities in (see Continuity
of functions)
domain of, 5.1 to 5.19, 5.24 to
5.31, 5.34 to 5.37, 9.16,
27.21, 41.64 to 41.66
even, 5.38, 5.40, 5.41,5.48, 5.53,
5.55,5.56,5.90,5.91,5.93,
8.46, 8.47, 15.31, 15.36,
15.46, 20.50, 38.73, 38.93
exponential (see Exponential
functions)
extrema of (see Extrema of
functions)
gamma, 32.22
greatest integer, 5.6, 5.7, 6.5
homogeneous multivariate, 42.74
to 42.80
hyperbolic (see Hyperbolic
functions)
increasing, 11.18, 11.20 to 11.26,
11.29, 11.48, 15.52
inflection points of, 13.2, 13.6,
13.7, 13.18, 13.20, 15.2,
15.3, 15.5, 15.7, 15.8, 15.10
to 15.19, 15.21, 15.25, 15.26,
15.32 to 15.35, 15.37, 15.40,
15.42 to 15.46, 15.48 to
15.51, 15.53, 15.57, 15.61
integrals of (see Integrals)
inverse, 5.69 to 5.74, 5.92, 5.93,
5.100,9.49
level surfaces of, 41.44 to 41.47
limits of (see Limits)
logarithmic (see Natural
logarithms)
Functions (Cont.):
maxima and minima of (see
Extrema of functions)
multivariate, 41.1 to 41.66
odd, 5.43, 5.44, 5.46, 5.49, 5.51,
5.52, 5.54 to 5.56, 5.90 to
5.92, 8.46, 8.47, 15.34,
15.47, 15.51, 20.48, 20.49,
24.97, 38.74, 38.93
one-one, 5.57, 5.58, 5.60, 5.63,
5.69 to 5.74, 5.92, 5.93,
5.100, 9.49
polynomial (see Polynomials)
range of, 5.1 to 5.19, 5.24 to
5.31, 5.34 to 5.37, 27.21
rational, integration of, 30.1 to
30.33
self-inverse, 5.69, 5.74, 5.75
of several variables, 41.1 to
41.66
strictly increasing, 11.48
strictly positive, 11.48
trigonometric (see Trigonometric
functions)
Fundamental theorem of calculus,
20.9 to 20.14
Gamma function, 32.22
Gauss' theorem, 45.49
Generalized mean value theorem,
11.38, 11.39
Geometric mean, 43.51
Geometric series, 37.5 to 37.9,
37.12, 37.13, 37.25, 37.26,
37.30 to 37.34, 37.45, 37.48,
37.67, 37.68, 37.73, 37.75,
37.77,37.83,37.91,37.113
to 37.116, 38.5, 38.26, 38.29
Gradient, 43.1 to 43.22, 43.56 to
43.64, 43.66, 43.67, 45.24,
45.32, 45.33, 45.35, 45.36,
45.39, 45.45
Graphs:
absolute extrema in, 15.31, 15.61
asymptotes in, 6.28 to 6.32,
15.17 to 15.19, 15.26, 15.39
to 15.43, 15.47, 15.48, 15.50,
15.52, 15.58, 15.59, 15.61
cardioids, 35.30, 35.34 to 35.36,
35.44, 35.66, 35.67, 35.69,
44.33, 44.38, 44.81
circles, 5.3, 34.1, 35.7 to 35.9,
35.13, 35.14, 35.17, 35.18,
35.41, 35.66, 35.67, 35.69,
35.87, 44.33, 44.37, 44.38,
44.42, 44.44
cones, 41.8, 41.10, 41.16
cubic functions, 5.10, 5.19, 41.34
cusps in, 15.44
cylinders, 41.1, 41.2