Unformatted text preview: p is a square. 2. Use Lagrange multipliers to prove that the triangle with maximum area that has a given perimeter p is equilateral. (Use Heron’s formula for the area A = p s ( s-x )( s-y )( s-z ) , where s = p/ 2, and x , y , z are the lengths of the sides). 3. Find the points on the sphere x 2 + y 2 + z 2 = 4 that are closest to and farthest from the point (3 , 1 ,-1). 4. The plane x + y + 2 z = 2 intersects the paraboloid z = x 2 + y 2 in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin....
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- Fall '08
- Math, Rectangle, Cuboid, largest rectangular box