;
second derivative of position or coordinate with respect to time:
Calculus Glossary
acceleration: First
derivative of velocity with
respect to time: ;
second derivative of position or coordinate with respect
to time:
antiderivative: The
antiderivative of a function f(x) is another function F(x). Finding the
antiderivative is
(loosely) reversing the process of differentiation. It
answers the question "What function do you
differentiate to produce f(x)?" In other words, if we
take the derivative of F(x) the result is f(x).
asymptote: a vertical or horizontal line on a graph which a function approaches.
critical number: a
number, c, in the domain of a function f(x) where the derivative,
f '(c), is 0 or does not
exist.
cubic: a polynomial in which
the highest power is the third power.
where 
definite integral of f(x)
on an interval (a,b): the result of evaluating the antiderivative,
F(x), at a and b and
subtracting: F(b) - F(a).
derivative: the limit of
as h approaches 0. Also, the ratio of a change in the
value of the function corresponding to a change
in the x-coordinate at which it is evaluated.
and 
is
given by 
extrema: plural for extreme point
extreme point: any of the maxima or minima of a function; f '(x) = 0 at an extreme point.
first
derivative test: the use of f '(x) = 0 to determine the location of
maxima, minima, or
points of inflection
indefinite integral: the notation
limit of f(x) at c: L
is the value of f(x)approaches as x gets closer to c from either the right
and the left.
Written as 
.
Said as "the limit of f(x), as x approaches c, is L".
limits of integration: the
values of x which determine the area involved in a definite interval.
See the Fundamental
Theorem of Calculus.
maxima: plural of maximum
maximum: a high point on
a graph of a function, relative to nearby points; a point with zero slope,
preceded
by points with positive slope and followed by points
with negative slope.
The second derivative (= the rate of change in the slope)
is negative at a maximum since the slope
changes to less positive or more negative values as you
move from left to right.
mean value theorem: for two points
(a, f(a) ) and ( b, f(b) ), on a continuous curve, there is a point c in
between where the slope f '(c) is the same as the slope,
m, of the line joining the two points.
In the diagram, the two points are (-1,1) and (2,4). The
slope, m, of the line connecting them is 1. The
point c turns out to be x = 0.5.
minima: the plural of minimum
minimum: a low point on a graph of a function, relative to nearby points; a point with zero slope, preceded by points with negative slope and followed by points with positive slope.
The second derivative (= the rate of change in the slope)
is positive at a maximum since the slope
changes to less negative or more positive values as you
move from left to right.
point of inflection:
a point on a curve where f '(x) and f ''(x) are
both 0. The tangent line to the curve is
horizontal at this point. In contrast to a maximum or
minimum, the slope has the same sign just to the
left and just to the right of the critical point.
In the diagram below, the tangent line is horizontal at
(0,1), and the slope of the curve is positive on
both sides of this point.
Polynomial: a
sum of powers of x: 
quadrant: one of four regions in the coordinate plane defined by the x and y axes
quadratic: a
polynomial in which the highest power is 2: 
,
where a is not zero.
quadratic formula: to
find x in 
we
use the formula
Rolle's Theorem: Stated loosely,
if a function crosses the x axis in two places, it must curve back in
between, so that there must be at least one point where
the first derivative is 0 and the tangent line is
horizontal, as shown in the figure below. There, f(-1)
is 0 and f(3) is zero. The point in between where
the first derivative is 0 is x = 1. Note that this point
won't always be halfway between the other two
points.
secant line: a line joining
two points on a curve, as in the figure 
second derivative: the derivative
of the first derivative: 
second derivative test: the use of the sign of the second derivative to identify extrema. The first derivative is 0 and the second derivative is positive at a relative minimum. The first derivative is 0 and the second derivative is negative at a relative maximum.
for a curve, the slope of the tangent line
tangent line: the steepest line in the diagram below
velocity:
first derivative of position with respect to time, 
.
Also the integral of the acceleration: 
