Page 294 - Calculus Workbook For Dummies

278 Calculus Workbook For Dummies

• D • unable to solve for y, 78–79
of variables raised to a power, 69
definite integral, 166–167, 274 difference quotient
degree/radian conversions, 23 definition, 61, 269
derivative-of-a-constant rule, 69 problems, 62–63
derivatives. See also curves; functions; rates; solutions, 64–67
slope differentiation. See also antiderivatives
absolute extrema, 98–101 acceleration, 131–134
compositions of functions, 75–77 average velocity, 132–134
concavity of curves, 102–105 displacement, 131
of constants, 69 distance, 131–134
definition, 59 linear approximation, 138–139
of derivatives, 80–81 lines, 134–137
difference quotient negative displacement, 131–134
definition, 61, 269 negative velocity, 131–134
problems, 62–63 normals, 134–137
solutions, 64–67 optimization, 124–126
first derivative test position, 131–134
curves, shape analysis, 269 problems, 124–139
local extrema, 91–94, 270 related rates, 127–130
rates, 269 rules for
sign changes, 270 chain, 75–77. See also implicit differentiation
slopes, 269 derivative of a constant, 69
highest/lowest points in curves, 98–101 high order derivatives, 80–81
hills and valleys in curves, 91–97 implicit differentiation, 78–79. See also chain
inflections points in curves, 102–105 rule
local extrema, 91–97 power, 69
Mean Value Theorem, 105–107 problems, 70–81
problems, 59–61, 92–107 product, 72–74
product of two functions, 72–74 quotient, 72–74
quotient of two functions, 72–74 solutions, 82–89
rate, calculating average, 105–107 solutions, 140–156
rules for speed, 132–134
chain, 75–77. See also implicit differentiation speed and distance traveled, 131–134
derivative of a constant, 69 tangents, 134–137
high order derivatives, 80–81 velocity, 131–134
implicit differentiation, 78–79. See also chain direct comparison test, 247–250
rule disk/washer method, 222–226
power, 69 displacement, 131
problems, 70–81 distance, 131–134
product, 72–74 divergence/convergence, testing for, 245–254
quotient, 72–74, 270–271
solutions, 82–89 • E •
second derivative test
concavity, 102, 270 estimation
inflection points, 102, 270 area under curves, 159–161, 168–170
local extrema, 95–97 linear approximation, 138–139, 271
slope, calculating average, 105–107 exact areas, 166
smiles and frowns, curve shape, 102–105 expressions with trigonometric functions,
solutions, 64–67, 108–121 196–198
symbol for, 7