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homework05_w12

# homework05_w12 - Math 215 Homework Set 5 14.715.2 Winter...

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Math 215 Homework Set 5: §§ 14.7–15.2 Winter 2012 Most of the following problems are modified versions of the problems from your text book, Multivariable Calculus , 7th ed., by James Stewart. Your solution to each problem should be complete, show all work, and be written in complete sentences where appropriate. For Maple problems, include a print-out that shows all of the work and graphs that you generated in Maple to solve the problem, in addition to any work you may have done by hand. 14.7.3: Consider a function of one variable, f ( x ) , which is continuous on an interval I . If f has a single critical point, x = a , in I , then if that point is a local maximum (or minimum) it must also be an absolute maximum. Explain why this is. Next, consider the function of two variables, g ( x, y ) = 3 xe y - x 3 - e 3 y . Note that this is continuous for all values of x and y . (a) Show that g ( x, y ) has a single critical point, and find it. (b) Show that g ( x, y ) has a local maximum at this point.

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