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Index Index

absolute extrema, Definition Paragraph
absolute maximum, Definition Definition
absolute minimum, Definition Definition
multivariate, Theorem
optimization, Paragraph
absolute value, Paragraph
properties, Paragraph
horizontal, Definition Paragraph
break-even point, Paragraph
break-even price, Paragraph
break-even quantity, Paragraph
Cartesian coordinates, Paragraph
central angle, Paragraph
chain rule
multivariate, Theorem
single variable, Theorem
Clairaut's theorem, Theorem
completing the square, Paragraph
concave down, Item
concave up, Item
concavity, Paragraph
circle, Paragraph
ellipse, Paragraph
horizontal hyperbola, Paragraph
horizontal parabola, Paragraph
standard form, Paragraph
vertical hyperbola, Paragraph
vertical parabola, Paragraph
consumer price index, Paragraph
contour map, Paragraph
average cost, Paragraph
constant cost, Paragraph
marginal cost, Paragraph
total cost, Paragraph
variable cost, Paragraph
critical point
single-variable!, Definition
two-variable, Definition
cross product, Paragraph
properties, Theorem
cylindrical coordinates, Paragraph
convert to rectangular, Paragraph
decrease, Paragraph
decreasing, Subsection
del (\(\nabla\)), Paragraph
delta notation, Paragraph Paragraph
demand curve, Paragraph
demand equation, Paragraph
acceleration, Paragraph
exponential function, Paragraph Paragraph
intervals of increase and decrease, Item
Leibniz notation, Paragraph
logarithmic function, Paragraph
n-th derivative, Paragraph
non-existence of derivative, Subsection
not differentiable, Subsection
of the inverse, Paragraph
rate of change, Paragraph
rules, Paragraph
chain rule, Theorem
constant multiple rule, Theorem
derivative of a constant function, Theorem
implicit differentiation, Paragraph
logarithmic differentiation, Paragraph
power rule, Theorem Example
product rule, Theorem
quotient rule, Theorem
sum and difference rules, Theorem
second derivative, Paragraph
trigonometric functions, Paragraph
velocity, Example Paragraph
derivative notation, Section
determinate form, Paragraph Definition
difference quotient, Paragraph
differentiable, Paragraph Definition
differentiable at a point, Definition
differentiable on an interval, Definition
differential operator, Section
differentials, Definition
differentiation, Paragraph
direction vector, Definition
directional derivative, Paragraph
discriminant, Theorem
distance formula, Subsection Paragraph
dot product, Paragraph
properties, Theorem
fundamental limit of calculus, Paragraph
elasticity of demand, Definition
elastic, Item
inelastic, Item
unitary, Item
elementary function, Paragraph
equilibrium point, Definition
equilibrium price, Definition
equilibrium quantity, Definition
absolute error, Paragraph
measurement error, Paragraph
percentage error, Paragraph
propagation error, Paragraph
relative error, Paragraph
Euler's constant, Paragraph
fundamental limit of calculus, Paragraph
extreme value theorem, Paragraph
Fermat's theorem, Paragraph
first derivative test, Paragraph
fixed cost, Paragraph
function, Paragraph
composition, Subsection
continuous, Paragraph
dependent variable, Paragraph
discontinuous, Paragraph
domain, Paragraph
elementary, Paragraph
even, Paragraph
exponential function, Paragraph
special base e, Paragraph
independent variable, Paragraph
infinite discontinuity, Paragraph
inverse, Paragraph
jump discontinuity, Paragraph
left continuous, Definition
linear, Paragraph
logarithmic function, Paragraph
multi-variable, Paragraph
natural logarithm, Paragraph
odd, Paragraph
of two variables, Paragraph
one-to-one, Paragraph
removable discontinuity, Paragraph Paragraph
right continuous, Definition
same derivative, Theorem
single-variable, Paragraph
symmetry, Paragraph
transcendental, Paragraph
global extrema, Paragraph
global extremum, Item
gradient, Paragraph
greatest integer, Exercise
implicit differentiation, Subsection
increase, Paragraph
increasing, Subsection
inequality notation, Paragraph
inflation rate, Paragraph
inflection point, Paragraph Definition
intermediate value theorem, Theorem Paragraph
internal rate of return, Paragraph
intersection, Paragraph
interval, Paragraph
closed interval, Paragraph
open interval, Paragraph
irrational, Paragraph
L'Hôpital's rule, Theorem
Lagrange multipliers, Paragraph
law of diminishing return, Paragraph
level curve, Paragraph
level set, Paragraph
level surface, Paragraph
at infinity, Definition
indeterminate form, Definition
infinite, Definition
left-hand, Definition
multivariate function, Definition
one-sided, Paragraph Paragraph
right-hand, Definition
line, Paragraph
direction vector, Definition
general form, Subsection
parametric equations, Definition
point-slope form, Paragraph
slope, Paragraph
slope-intercept form, Paragraph
vector equation, Definition
y-intercept, Paragraph
linear approximation, Paragraph Item
linearization, Paragraph Item
local extremum, Item
logarithmic differentiation, Subsection
marginal, Paragraph
marginal average cost function, Paragraph
marginal cost function, Paragraph
marginal profit function, Paragraph
marginal revenue function, Paragraph
marginal analysis, Paragraph
market equilibrium, Paragraph
equilibrium price, Paragraph
equilibrium quantity, Paragraph
mean value theorem, Paragraph Theorem
midpoint, Paragraph
multi-variable, Paragraph
Newton's method, Paragraph Paragraph
stationary point, Item
unstable, Item
normal vector, Paragraph
number systems, Paragraph
complex numbers, Paragraph
integers, Paragraph
natural numbers, Paragraph
rational numbers, Paragraph
real numbers, Paragraph
parametric equations, Paragraph
partial derivatives
first-order partial derivatives, Definition
mixed partial derivatives, Item
second-order partial derivatives, Paragraph
partial deriviatives
first-order partial derivatives, Paragraph
normal vector, Paragraph
scalar equation of plane, Definition
point of diminishing return, Paragraph
polar coordinates, Paragraph
convert to rectangular, Paragraph
of two variables, Paragraph
predator-prey population model, Paragraph
production function, Paragraph
Cobb-Douglas production function, Paragraph
marginal productivity of capital, Paragraph
marginal productivity of labour, Paragraph
profit function, Paragraph
quadratic formula, Subsection
radians, Paragraph
rate of change, average, Item
rate of change, instantaneous, Section
rationalizing, Paragraph
related rates problems, Paragraph
relative demands, Paragraph
competitive commodities, Definition
complementary commodities, Definition
partial derivatives, Item
relative demand equations, Definition
relative extrema, Paragraph
multivariate, Item
relative maximum, Paragraph Item Definition
relative minimum, Paragraph Item Definition
revenue function, Paragraph
rolle's theorem, Theorem
saddle point, Item Definition
secant line, Section
second derivative
inflection point, Paragraph
second derivative test, Paragraph
concave down, Item
concave up, Item
concavity, Theorem
relative extrema, Paragraph Item
set, Paragraph
single-variable, Paragraph
measure of sensitivity, Section
slope of secant line, Definition
difference quotient, Item
rate of change, average, Item
slope of tangent line, Section
rate of change,instantaneous, Section
sphere, Definition
equation of sphere, Definition
spherical coordinates, Paragraph
convert to rectangular, Paragraph
squeeze theorem, Paragraph
subset, Paragraph
supply curve, Paragraph
supply equation, Paragraph
symmetry, Paragraph
even, Definition
tangent line, Section Paragraph
tangent line equation, Definition
tangent plane, Definition
transcendental function, Paragraph
transformations, Paragraph
triangle inequality, Item
amplitude, Item
arccosine, Example
arcsine, Paragraph
arcsine function, Definition
arctangent, Example
CAST rule, Paragraph Subsection
cosecant, Item
cosine, Item
cotangent, Item
identities, Paragraph
inverse sine function, Definition
period, Item Item
secant, Item
sine, Item
special triangles, Paragraph
tangent, Item
undefined, Paragraph
union, Paragraph
unit circle, Paragraph
unit vector, Paragraph
vector, Paragraph
angle between, Paragraph
anti-parallel, Item
parallel, Item
perpendicular, Item
projection, Paragraph
scalar multiplication, Paragraph
scalar projection, Paragraph
sum, Paragraph