## Index Index

absolute extrema, Definition Paragraph

absolute maximum, Definition Definition

absolute minimum, Definition Definition

multivariate, Theorem

optimization, Paragraph

absolute value, Paragraph

properties, Paragraph

asymptote

horizontal, Definition Paragraph

slant, Definition Paragraph

vertical, Definition 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

conics

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

cost

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

demand curve, Paragraph

demand equation, Paragraph

derivative, Paragraph Definition Paragraph

acceleration, 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

product rule, Theorem

quotient rule, Theorem

sum and difference rules, Theorem

second derivative, Paragraph

trigonometric functions, 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

error

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

right continuous, Definition

same derivative, Theorem

single-variable, Paragraph

symmetry, Paragraph

transcendental, Paragraph

implicit differentiation, Subsection

increase, Paragraph

increasing, Subsection

indeterminate form, Paragraph Paragraph Definition Definition

inequality notation, Paragraph

inflation rate, Paragraph

inflection point, Paragraph Definition

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

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

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

midpoint, Paragraph

multi-variable, 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

plane

normal vector, Paragraph

scalar equation of plane, Definition

point of diminishing return, Paragraph

polar coordinates, Paragraph

convert to rectangular, Paragraph

polynomial

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

set, Paragraph

single-variable, Paragraph

slope

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

odd, Definition

tangent line equation, Definition

tangent plane, Definition

transcendental function, Paragraph

transformations, Paragraph

triangle inequality, Item

trigonometry

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

inverses, Definition Definition

secant, Item

sine, Item

special triangles, Paragraph

tangent, Item