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