Calculus Vocabulary Review
Concave Down
2nd derivative is negative.
Concave Up
2nd derivative is positive.
Tangent Line
A line that touches a curve at a point without crossing the curve
Critical Point
A point on the graph of the function at which the derivative is either zero or undefined.
Local Extrema
A point on the graph where there is a peak or valley.
Optimization
A process that maximizes or minimizes a quantity
Second Derivative Test
Allows you to find where functions are concave up or down. Also allows you to find points of inflection.
First Derivative Test
Allows you to find where functions are increasing and decreasing. Also allows you to find relative extrema.
Limit
As x approaches a number, what is f(x) approaching.
Velocity Function
Average rate of change of position function. Rate of change of distance over time.
Interval notation
Brackets- include end points Parentheses- do not include end points
Instantaneous Velocity
Derivative of position function. Velocity of object at specific point in time.
Acceleration Function
Derivative of the velocity function.
Removable Discontinuity
Ex. Hole in graph. Function can be made continuous by redefining f(x).
Non-Removable Discontinuity
Ex. Vertical asymptote
Decreasing Function
Function that is falling from left to right.
Increasing Function
Function that is rising from left to right.
Derivative
Gives formula to find slope of tangent line to a curve at any point on curve.
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.
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.
Extreme Value Theorem
If f is continuous on [a,b], then there is a max and a min
Point of Tangency
Point where tangent line intersects curve
Relative Maximum
The highest point in a particular section of the graph
Absolute Maximum
The highest point of the graph.
Relative Minimum
The lowest point in a particular section of the graph
Absolute Minimum
The lowest point of the graph.
Calculus
The mathematical study of change.
Point of Inflection
The point where the concavity of a function changes.
Differentiation
The process of finding the derivative.
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.
Domain
X-values (inputs)
Range
y-values (Outputs)
