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Unformatted text preview: maximum of f. ◦ If f '(x) < 0 for all x in (a, c) and f '(x) > 0 for all x in (c, b), then c is a local minimum of f. Example: Determine the intervals on which the function is increasing or decreasing and the local maximums and local minimums. Since the domain of f is the same as the domain of f', 4 is the only critical number of f. Testing: By the First Derivative Test, x = 4 is a local minimum. Example: ◦ Since the domain of f is the same as the domain of f', 3 and 6 are the only critical numbers of f. ◦ Testing: x < 3 f'(10) = 672 f is increasing 3 < x < 6 f(0) = 108 f is decreasing x >6 f(10) = 312 f is increasing By the First Derivative Test, x = 3 is a local minimum and x = 6 is a local maximum. x < 4 f'(0) = 8 f is decreasing x > 4 f'(5) = 2 f is increasing...
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This note was uploaded on 03/18/2011 for the course MATH 032 taught by Professor Junghenn during the Fall '08 term at GWU.
 Fall '08
 JUNGHENN
 Calculus, Mean Value Theorem

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