Definitions Theorems
What is a Limit?
The value that a function or expression approaches as the domain variable(s) approach a specific value.
What is the Mean Value Theorem?
A major theorem of calculus that relates values of a function to a value of its derivative. Essentially the theorem states that for a "nice" function, there is a tangent line parallel to any secant line.
What is the Second Derivative test?
A method for determining whether a critical point is a relative minimum or maximum.
What is the Fundamental Theorem of Calculus?
The theorem that establishes the connection between derivatives, antiderivatives, and definite integrals. The fundamental theorem of calculus is typically given in two parts.
What is a Critical Point?
A point (x, y) on the graph of a function at which the derivative is either 0 or undefined.
What is the Extreme Value Theorem?
A theorem which guarantees the existence of an absolute max and an absolute min for any continuous function over a closed interval.
What is Differentiable?
A curve that is smooth and contains no discontinuities or cusps.
What is Intermediate Value Theorem?
A theorem verifying that the graph of a continuous function is connected.
What is a Inflection Point?
A point at which a curve changes from concave up to concave down, or vice-versa.
What is Rolle's Theorem?
A theorem of calculus that ensures the existence of a critical point between any two points on a "nice" function that have the same y-value.

Calculus Edition

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