Thursday October 4 Constrained min max via Lagrange multipliers 1 Let C be the curve in R2 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 x y 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 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 3x x 3 2y 2 y 4 Use the formula for f and the 2nd 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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