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Unformatted text preview: f ’(x) = 0 or f ’ (x) DNE • Relative Extrema: A function f has a relative maximum at x = c if there is an open interval (a,b) containing c such that f(x) < f(c) for all x in (a,b) • A function f has a relative minimum at x = c if there is an open interval (a,b) containing c such that f(x) > f(c) for all x in (a,b) To find Relative Extrema: 1 st derivative test • 1. Determine the Critical Numbers of f(x) • 2. Determine the sign of f ’(x) to the left and to the right of each critical number. • 3. If f ’(x) changes sign from positive to negative across the critical number, f(c) is a relative maximum. • 4. If f ’(x) changes sign from negative to positive across the critical number, f(c) is a relative minimum. • 5.If f ‘(x) does not change sign across the critical number, then f(c) is not a local extremum. • Let f(t) = 2t / (t 2 +1) . Determine the t value of any relative extrema....
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 Spring '08
 VAUGHN
 Calculus, Critical Point, Derivative, Fermat's theorem

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