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AP Calculus 2- Understanding the Derivative

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Section 1

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Concave down

Front

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Calculus Math

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6 years ago

Date created

Mar 14, 2020

Cards (30)

Section 1

(30 cards)

Concave down

Front

A graph or part of a graph which looks like an upside-down bowl or part of an upside-down bowl.

Back

Concave up

Front

A graph or part of a graph which looks like a right-side up bowl or part of an right-side up bowl.

Back

Average Rate of Change

Front

The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph.

Back

Cusp

Front

A sharp point on a curve, that is not differentiable.

Back

Power Rule

Front

The formula for finding the derivative of a power of a variable.

Back

Decreasing Function

Front

A function with a graph that moves downward as it is followed from left to right. For example, any line with a negative slope.

Back

Critical Number

Front

The x-value of a critical point.

Back

Discontinuity

Front

A point at which the graph of a relation or function is not connected.

Back

Tangent Line

Front

A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.

Back

Constant Term

Front

The term in a simplified algebraic expression or equation which contains no variable(s).

Back

Continuously Differentiable Function

Front

A function which has a derivative that is itself a continuous function.

Back

IVT

Front

A theorem verifying that the graph of a continuous function is connected.

Back

Relative Maximum

Front

Where the function has a horizontal tangent line and the derivative graph goes from positive to negative.

Back

Second Derivative

Front

The derivative of a derivative. Usually written f"(x) or y".

Back

Instantaneous Rate of Change

Front

The rate of change at a particular moment. Same as the value of the derivative at a particular point.

Back

Derivative

Front

A function which gives the slope of a curve; that is, the slope of the line tangent to a function.

Back

Limit

Front

The value that a function or expression approaches as the domain variable(s) approach a specific value.

Back

Calculus

Front

The branch of mathematics dealing with limits, derivatives, definite integrals, indefinite integrals, and power series.

Back

Cartesian Form

Front

A function (or relation) written using (x, y) or (x, y, z) coordinates.

Back

Extremum

Front

An extreme value of a function. In other words, the minima and maxima of a function

Back

Increasing Function

Front

A function with a graph that goes up as it is followed from left to right.

Back

Curve

Front

A word used to indicate any path, whether actually curved or straight, closed or open.

Back

Relative Minimum

Front

Where the function has a horizontal tangent line and the derivative graph goes from negative to positive.

Back

Asymptote

Front

A line or curve that the graph of a relation approaches more and more closely the further the graph is followed.

Back

Bounded Function

Front

A function with a range that is a bounded set. The range must have both an upper bound and a lower bound.

Back

Critical Point

Front

A point (x, y) on the graph of a function at which the derivative is either 0 or undefined.

Back

Infinity

Front

A "number" which indicates a quantity, size, or magnitude that is larger than any real number.

Back

Continuous Function

Front

A function with a connected graph.

Back

Normal Line

Front

Perpendicular to the tangent line

Back

First derivative test

Front

A method for determining whether an inflection point is a minimum, maximum, or neither.

Back