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.

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.

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

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

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

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

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

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

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.

The process for finding the derivative of a composite function.

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

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)).

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

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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.

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

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

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

The process of finding the derivative of a 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.

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

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

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

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

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.

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.

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

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.

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

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

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.

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.

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

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

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

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

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).