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Unformatted text preview: The limit of f(x) as x approaches c must exist and be equal to f(c). (If the point c in the domain of f is not an accumulation point of the domain, then this condition is vacuously true, since x cannot approach c. Thus, for example, every function whose domain is the set of all integers is continuous, merely for lack of opportunity to be otherwise. However, one does not usually talk about continuous functions in this setting.) Relative Maximum:- The highest point in a particular section of a graph. The highest value of y. Relative Minimum:- See above Inflection Points:- An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes Concavity:- Let f ( x ) be a differentiable function on an interval I . Assume that f '( x ) is also differentiable on I . (i) f ( x ) is concave up on I iff on I . (ii) f ( x ) is concave down on I iff on I ....
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- Fall '06