09extreme values and mvt_solns

09extreme values and mvt_solns - Calculus (MAT 220) -...

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Calculus (MAT 220) - Extreme Values and MVT (Solutions) Extreme values 1. Sketch the graph of a function that satisﬁes each of the following (ﬁve diﬀerent functions): (a) f attains both a maximum and a minimum on [0 , 5] and is con- tinuous on [0 , 5]. - 4 - 2 2 4 5 10 15 20 25 30 35 (b) f attains both a maximum and a minimum on [0 , 5] and is not continuous on [0 , 5]. - 4 - 2 2 4 2 4 6 8 (c) f attains a maximum but not a minimum on [0 , 5]. At what points of [0 , 5] is your function not continuous? 1

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1 2 3 4 5 1 2 3 4 5 (d) f attains a minimum but not a maximum on [0 , 5]. At what points of [0 , 5] is your function not continuous? 1 2 3 4 5 1 2 3 4 5 (e) f attains neither a maximum nor a minimum on [0 , 5]. At what points of [0 , 5] is your function not continuous? 2
1 2 3 4 5 1 2 3 4 5 2. For each of the following, ﬁnd the absolute maximum and absolute minimum values of the function on the given interval. (a)

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This note was uploaded on 09/02/2010 for the course MATH SMUD 206 taught by Professor Condon during the Spring '10 term at UMass (Amherst).

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09extreme values and mvt_solns - Calculus (MAT 220) -...

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