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Home  Continuous Functions Maxima and Minima Definition |
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Definition
Let us assume throughout this section that f is a real function whose domain is an interval f, and furthermore that f is continuous on I. A problem that often arises is that of finding the point c where f(c) has its largest value, and also the point c where f(c) has its smallest value. The derivative turns out to be very useful in this problem. We begin by defining the concepts of maximum and minimum. DEFINITION Let c be a real number in the domain I of f. (i) f has a maximum at c if f(c) ≥ f(x) for all real numbers x in I. In this case f(c) is called the maximum value of f. (ii) f has a minimum at c if f(c) ≤ f(x) for all real numbers x in I. f(c) is then called the minimum value of f.
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Last Update: 2006-11-25