Printable Calculus Vocabulary flash cards

antiderivative

a representation, usually in symbolic form, of any function whose derivative is a given function.

tangent

a line or a plane that touches a curve or a surface at a single point.

chain rule

the theorem that defines the method for taking the derivative of a composite function.

concave downward

part of a graph resembling an upside down bowl.

concave upward

part of a graph resembling a right side up bowl.

continuous

being in immediate connection or spatial relationship.

critical point

point on the graph where the derivative is either 0 or undefined.

cylindrical shell method

technique for finding the volume of a solid of revolution.

definite integral

the representation of the difference in values of a primitive of a given function evaluated at two designated points.

derivative

the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

differentiable

a function whose graph is curve that is smooth and contains no discontinuities or cusps.

disk method

technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

extreme value theorem

guarantees an absolute max and an absolute min

first derivative test

determines whether an inflection point is a minimum, maximum, or neither.

higher order derivatives

any derivatives beyond the first derivative.

implicit differentiation

method for finding the derivative of an implicitly defined function or relation using the chain rule.

indefinite integral

another way of saying antiderivative.

instantaneous rate of change

rate of change at a particular moment.

instantaneous velocity

rate at which an object is moving at a particular moment.

integration by parts

a method of evaluating an integral by use of the formula, ∫udv = uv − ∫vdu.

limit

value that a function approaches as the domain variable approach a specific value.

mean value theorem

the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

normal line

line that is at a 90 degree angle, perpendicular to a surface.

point-slope form

form used the most when finding the equation of a line.

riemann sum

method for approximating the definite integral.

second derivative test

determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

u-substitution

integration method that involves using the chain rule in reverse.

trigonometric substitution

substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

washer method

similar to the disk method but using washers instead of disks.

antiderivative

a representation, usually in symbolic form, of any function whose derivative is a given function.

tangent

a line or a plane that touches a curve or a surface at a single point.

chain rule

the theorem that defines the method for taking the derivative of a composite function.

concave downward

part of a graph resembling an upside down bowl.

concave upward

part of a graph resembling a right side up bowl.

continuous

being in immediate connection or spatial relationship.

critical point

point on the graph where the derivative is either 0 or undefined.

cylindrical shell method

technique for finding the volume of a solid of revolution.

definite integral

the representation of the difference in values of a primitive of a given function evaluated at two designated points.

derivative

the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

differentiable

a function whose graph is curve that is smooth and contains no discontinuities or cusps.

disk method

technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

extreme value theorem

guarantees an absolute max and an absolute min

first derivative test

determines whether an inflection point is a minimum, maximum, or neither.

higher order derivatives

any derivatives beyond the first derivative.

implicit differentiation

method for finding the derivative of an implicitly defined function or relation using the chain rule.

indefinite integral

another way of saying antiderivative.

instantaneous rate of change

rate of change at a particular moment.

instantaneous velocity

rate at which an object is moving at a particular moment.

integration by parts

a method of evaluating an integral by use of the formula, ∫udv = uv − ∫vdu.

limit

value that a function approaches as the domain variable approach a specific value.

mean value theorem

the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

normal line

line that is at a 90 degree angle, perpendicular to a surface.

point-slope form

form used the most when finding the equation of a line.

riemann sum

method for approximating the definite integral.

second derivative test

determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

u-substitution

integration method that involves using the chain rule in reverse.

trigonometric substitution

substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

washer method

similar to the disk method but using washers instead of disks.