408DS09assign10 - aquarium that minimize the cost of the...

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M408D Spring 2009 Assignment 10 Due Thursday, April 23 Be sure that you have read and understood sections 15.6, 15.7, and 15.8 and worked the assigned text exercises before you complete this assignment. 1. The plane y + z = 3 intersects the cylinder x 2 + y 2 = 5 in an ellipse. Find parametric equations for the tangent line to this curve a at the point ( - 1 , 1 , 2). 2. Find all local extrema and saddle points for the function f ( x,y ) = 2 x 3 + xy 2 + 5 x 2 + y 2 . 3. The base of an aquarium with given volume V is made of slate and the sides are made of glass. (There is no top to the aquarium.) If the slate costs 5 times as much (per unit area) as the glass, find the dimensions of the
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Unformatted text preview: aquarium that minimize the cost of the materials. (For this problem, you may assume that the absolute minimum occurs at a critical point.) 4. Find the absolute maximum and the absolute minimum of the function f ( x,y ) = xy 2 on the set D = { ( x,y ) | x ,y ,x 2 + y 2 3 } . 5. Find the volume of the largest rectangular box that can be inscribed in the ellipsoid 9 x 2 + 36 y 2 + 4 z 2 = 36. (To be inscribed in the ellipsoid means that all vertices of the box lie on the ellipsoid. ) 1...
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