MATH 140 Lecture Notes - Lecture 13: Maxima And Minima, Horse Length
Document Summary
Math 140 - lecture 13 - maximum and minimum values. Let c be a number in the domain d of a function f. Absolute minimum value of f f on d if on d if f (c) f (x) f (c) f (x ) for all x in d for all x in d. An absolute maximum or minimum is sometimes called a global maximum or minimum. The number f (c) is a f are called extreme values of f. Local minimum value of f f if if f (c) f (x ) f (c) f (x ) when x is near c when x is near c. Example: the function f (x)=cos x takes on its (local and absolute) maximum value of 1 infinitely many times, since cos2 n=1 for any integer n and. 1 cos x 1 for all x cos(2n+1) = 1 is its minimum value, where n is any integer.
