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Chapter 5.1-Extreme Values - Theorem • If f(c is a local...

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F(x) has a Global (absolute) max (or minnimum) IFF f(c) >= f(x) for all of the values on the domain F(x) has a Local (relative) max (or min) IFF f(c)>=f(x) for all values of x in some open interval containing c Extreme Value Theorem: If f is continuous on a closed interval [a,b] then f must have both a global max and a global min
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Unformatted text preview: Theorem • If f(c) is a local max/min point and f'(c) exists, then f'(c) = 0 (turning point) ◦ Critical Point • Def: any point in the interior of the domain where the derivative f'(c) = 0 or ◦ f'(c) = DNE When looking for max or min points, we must check all of the critical points ◦ and the endpoints...
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