Maximum and minimum

Maximum and minimum - MAXIMUM AND MINIMUM VALUES One of the...

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Unformatted text preview: MAXIMUM AND MINIMUM VALUES One of the most important applications of differential calculus is the optimiza- tion. Optimization problems can be reduced to finding the maximum or minimum values of a function. Definition 1. A function f has an absolute (global) maximum at c if f ( c ) ≥ f ( x ) for all x in the domain of f . The number f ( c ) is called the maximum value of f on the domain. Similarly, f has an absolute (global) minimum at c if f ( c ) ≤ f ( x ) for all x in the domain of f . The number f ( c ) is called the minimum value of f on the domain. The maximum and minimum values of f are called the extreme values of f . Definition 2. A function f has an local (relative) maximum at c if f ( c ) ≥ f ( x ) when x is near c . Similarly, f has an local (relative) minimum at c if f ( c ) ≤ f ( x ) when x is near c . The following theorem guarantees that some functions must have extreme values....
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Maximum and minimum - MAXIMUM AND MINIMUM VALUES One of the...

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