Calculus 1 Vocabulary Review

Calculus

The mathematical study of change.

Interval notation

Brackets- include end points

Parentheses- do not include end points

Domain

X-values (inputs)

Range

y-values (Outputs)

Derivative

Gives formula to find slope of tangent line to a curve at any point on curve.

Differentiation

The process of finding the derivative.

Velocity Function

Average rate of change of position function. Rate of change of distance over time.

Acceleration Function

Derivative of the velocity function.

Instantaneous Velocity

Derivative of position function. Velocity of object at specific point in time.

Limit

As x approaches a number, what is f(x) approaching.

Left-hand Limit

The value that a function is approaching as x approaches a given value from values less than x.

Right-hand Limit

The value that a function is approaching as x approaches a given value from values more than x.

Increasing Function

Function that is rising from left to right.

Decreasing Function

Function that is falling from left to right.

Absolute Maximum

The highest point of the graph.

Absolute Minimum

The lowest point of the graph.

Relative Maximum

The highest point in a particular section of the graph

Relative Minimum

The lowest point in a particular section of the graph

Local Extrema

A point on the graph where there is a peak or valley.

Critical Point

A point on the graph of the function at which the derivative is either zero or undefined.

Concave Down

2nd derivative is negative.

Concave Up

2nd derivative is positive.

Point of Inflection

The point where the concavity of a function changes.

First Derivative Test

Allows you to find where functions are increasing and decreasing. Also allows you to find relative extrema.

Second Derivative Test

Allows you to find where functions are concave up or down. Also allows you to find points of inflection.

Mean Value Theorem

If a function is continuous over a closed interval and differentiable over an open interval from a to b, then there exists a number c where the average rate of change equals the instantaneous rate of change.

Rolle's Theorem

If a function is continuous over a closed interval and differentiable over an open interval from a to b and f(a) = f(b), then there exists at least one critical number in the open interval from a to b.

Non-Removable Discontinuity

Ex. Vertical asymptote

Removable Discontinuity

Ex. Hole in graph. Function can be made continuous by redefining f(x).

Optimization

A process that maximizes or minimizes a quantity

Tangent Line

A line that touches a curve at a point without crossing the curve

Point of Tangency

Point where tangent line intersects curve

Extreme Value Theorem

If f is continuous on [a,b], then there is a max and a min