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# Worksheet_7 - S that are closest to(4,2,0 4 For the...

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Discussion — Thursday, September 30th Subject: Constrained min/max via Lagrange multipliers. 1. Let C be the curve in R 2 given by x 3 + y 3 = 16. (a) Sketch the curve C . (b) Is C bounded? (c) Is C closed? 2. Consider the function f ( x , y ) = e xy on C . (a) Is f continuous? What does the Extreme Value Theorem tell you about the existance of global min and max of f on C ? (b) Use Lagrange multipliers to determine both the min and max values of f on C . 3. Consider the surface S given by z 2 = x 2 + y 2 (a) Sketch S . (b) Use Lagrange multipliers to ﬁnd the points on

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Unformatted text preview: S that are closest to (4,2,0). 4. For the function shown on the back of the sheet, use the level curves to ﬁnd the locations and types (min/max/saddle) for all the critical points of the function: f ( x , y ) = 3 x-x 3-2 y 2 + y 4 Use the formula for f and the 2 nd-derivative test to check your answer. 5. If the length of the diagonal of a rectangular box must be L , what is the largest possible volume?...
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Worksheet_7 - S that are closest to(4,2,0 4 For the...

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