## MA.912.C.5.1 - Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions and solving applications related to motion along a line.

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### Math Definitions Collection--Calculus Concepts

This collection aggregates all the definitions for key terms in a standards Calculus course. There are a total of 88 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation. Calculus Vocabulary

### Definition--Calculus Topics--Absolute Maximum

Definition--Calculus Topics--Absolute Maximum

When a function takes an input value, a, for some value in the domain, such that f(a) ≥ f(x), for all x in the domain.

Calculus Vocabulary

### Definition--Calculus Topics--Absolute Minimum

Definition--Calculus Topics--Absolute Minimum

When a function takes an input value, a, for some value in the domain, such that f(a) ≤ f(x), for all x in the domain.

Calculus Vocabulary

### Definition--Calculus Topics--Absolute Value Function

Definition--Calculus Topics--Absolute Value Function

A piecewise function whose simplest form is shown below. These functions are not differentiable at their vertex.

Calculus Vocabulary

### Definition--Calculus Topics--Acceleration

Definition--Calculus Topics--Acceleration

The second derivative, with respect to time, for the displacement function. Acceleration is a vector quantity.

Calculus Vocabulary

### Definition--Calculus Topics--Antiderivative

Definition--Calculus Topics--Antiderivative

For two differentiable functions f(x) and F(x), if F'(x) = f(x), then F(x) is the antiderivative of f(x).

Calculus Vocabulary

### Definition--Calculus Topics--Area Beneath a Curve

Definition--Calculus Topics--Area Beneath a Curve

For a definite integral, it is the numerical result of the integration.

Calculus Vocabulary

### Definition--Calculus Topics--Asymptote

Definition--Calculus Topics--Asymptote

A line that the graph of a function approaches but does not intersect. Asymptotes can be vertical, horizontal, or oblique.

Calculus Vocabulary

### Definition--Calculus Topics--Average Rates of Change

Definition--Calculus Topics--Average Rates of Change

The ratio along an interval of a domain for a given function, comparable to calculating the slope of a line.

Calculus Vocabulary

### Definition--Calculus Topics--Ceiling Function

Definition--Calculus Topics--Ceiling Function

A discrete function that takes real number values and whose output is the least integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary

### Definition--Calculus Topics--Chain Rule

Definition--Calculus Topics--Chain Rule

The process for finding the derivative of a composite function.

Calculus Vocabulary

### Definition--Calculus Topics--Change of Variables

Definition--Calculus Topics--Change of Variables

A substitution technique where a variable replaces a more complicated expression. In calculus it can simplify differentiation or integration.

Calculus Vocabulary

### Definition--Calculus Topics--Composite Function

Definition--Calculus Topics--Composite Function

A function whose input values are made up of another function. For two functions f(x) and g(x), a composite function can be written as f(g(x)).

Calculus Vocabulary

### Definition--Calculus Topics--Concave Function

Definition--Calculus Topics--Concave Function

A function whose graph curves down along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary

### Definition--Calculus Topics--Continuous Functions

Definition--Calculus Topics--Continuous Functions

A function is continuous if it has no gaps along the domain of the function.

Calculus Vocabulary

### Definition--Calculus Topics--Convex Function

Definition--Calculus Topics--Convex Function

A function whose graph curves up along an interval of the domain. The inflection point is where the first derivative is zero.

Calculus Vocabulary

### Definition--Calculus Topics--Definite Integral

Definition--Calculus Topics--Definite Integral

The integral of a function with specific limits on the endpoints. A definite integral results in a numerical value.

Calculus Vocabulary

### Definition--Calculus Topics--Delta x

Definition--Calculus Topics--Delta x

The change in x-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary

### Definition--Calculus Topics--Delta y

Definition--Calculus Topics--Delta y

The change in y-coordinates for a given function. Often used in the formula for finding the derivative of a function.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative

Definition--Calculus Topics--Derivative

A function used to find the slope of a tangent to a curve at a given point. The derivative is based on the following limit.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Composite Function

Definition--Calculus Topics--Derivative of a Composite Function

For two functions f(x) and g(x), the derivative of the composite function f(g(x)) is f'(x)*g'(x). This is an example of the Chain Rule.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Linear Function

Definition--Calculus Topics--Derivative of a Linear Function

The derivative of a linear function of the form y = mx + b is the slope of the line, m.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Logarithmic Function

Definition--Calculus Topics--Derivative of a Logarithmic Function

The derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Polynomial Function

Definition--Calculus Topics--Derivative of a Polynomial Function

The derivative of a polynomial of degree n is another polynomial of degree n - 1.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Quadratic Function

Definition--Calculus Topics--Derivative of a Quadratic Function

Since a quadratic function is a polynomial function of degree 2, the derivative is a linear function.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Rational Function

Definition--Calculus Topics--Derivative of a Rational Function

Since a rational function is the ratio of two polynomials, the derivative of a rational function is also the ratio of two polynomials.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of a Trig Function

Definition--Calculus Topics--Derivative of a Trig Function

The derivative of a trig function is another trig function, as shown in the table.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of an Exponential Function

Definition--Calculus Topics--Derivative of an Exponential Function

The derivative of an exponential function is the product of the function and the natural log of the base. The derivative of ex is ex.

Calculus Vocabulary

### Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Use implicit differentiation and the quotient rule to find the derivative of an inverse trig function.

Calculus Vocabulary

### Definition--Calculus Topics--Differentiable Function

Definition--Calculus Topics--Differentiable Function

A function is differentiable if a derivative can be found at each point in its domain.

Calculus Vocabulary

### Definition--Calculus Topics--Differential Equation

Definition--Calculus Topics--Differential Equation

An equation that includes the derivative of a function f(x) and the variable x.

Calculus Vocabulary

### Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Calculus Vocabulary

### Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Calculus Vocabulary

### Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Calculus Vocabulary

### Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point.

Calculus Vocabulary

### Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Calculus Vocabulary

### Definition--Calculus Topics--Even Function

Definition--Calculus Topics--Even Function

A function whose graph is symmetric about the y-axis.

Calculus Vocabulary

### Definition--Calculus Topics--Explicit Function

Definition--Calculus Topics--Explicit Function

A function in which y can be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.<

Calculus Vocabulary

### Definition--Calculus Topics--Extreme Value Theorem

Definition--Calculus Topics--Extreme Value Theorem

For function f(x) along an interval, there are maximum and minimum values. If the derivative is zero along this interval, this is an inflection point.

Calculus Vocabulary

### Definition--Calculus Topics--First Derivative

Definition--Calculus Topics--First Derivative

For differentiable function f(x), the first derivative is denoted as f'(x).

Calculus Vocabulary

### Definition--Calculus Topics--Floor Function

Definition--Calculus Topics--Floor Function

A discrete function that takes real number values and whose output is the greatest integer value greater than the input value. The graph looks like a staircase.

Calculus Vocabulary

### Definition--Calculus Topics--Fundamental Theorem of Calculus

Definition--Calculus Topics--Fundamental Theorem of Calculus

The theorem that relates differentiation and integration. The two operations are basically inverses of each other.

Calculus Vocabulary

### Definition--Calculus Topics--Hooke's Law

Definition--Calculus Topics--Hooke's Law

A second-order differential equation that is used to model simple harmonic motion using a trigonometric function.

Calculus Vocabulary

### Definition--Calculus Topics--Horizontal Asymptote

Definition--Calculus Topics--Horizontal Asymptote

A horizontal line that the graph of a function approaches but does not intersect. The equation of a horizontal asymptote is y = c, for some constant c.

Calculus Vocabulary

### Definition--Calculus Topics--Implicit Differentiation

Definition--Calculus Topics--Implicit Differentiation

When a function cannot be written in the form of y as a function of x, then implicit differentation can be used to find the derivative with respect to x.<

Calculus Vocabulary

### Definition--Calculus Topics--Implicit Function

Definition--Calculus Topics--Implicit Function

A function in which y cannot be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equatio

Calculus Vocabulary

### Definition--Calculus Topics--Indefinite Integral

Definition--Calculus Topics--Indefinite Integral

The integral of a function without a specific limit on the endpoints. The result of an indefinite integral is a differentiable function.

Calculus Vocabulary

### Definition--Calculus Topics--Inflection Point

Definition--Calculus Topics--Inflection Point

The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve.

Calculus Vocabulary

### Definition--Calculus Topics--Instantaneous Rate of Change

Definition--Calculus Topics--Instantaneous Rate of Change

Another way of describing the slope of the line tangent to a given curve at a given point.

Calculus Vocabulary

### Definition--Calculus Topics--Integral

Definition--Calculus Topics--Integral

A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x).

Calculus Vocabulary