Maximum and Minimum Values Calculus III.

0:00 Definition: Maximum and Minimum Values in two Dimensions: "Local and Absolute".

2:29 Critical Points.

4:42 Example; f ( x, y ) = x^2 + y^2 -2x -6 y +14 " An Elliptic Paraboloid with a Vertex ( 1, 3, 4)" .

10:37 Example; Find the Extreme Values of f (x, y ) = y^2 - x^2: A Hyperbolic Paraboloid"; and Saddle Points.

16:32 Second Derivative Test.

20:47 Example; Find the Local Maximum and Minimum Values and Saddle Points of f ( x, y ) = x^4 + y^4 -4xy +1

27:11 Example; Find the Shortest Distance from the Point ( 1, 0, -2 ) to the Plane x + 2y +z = 4.

34:22 Example; A Rectangular Box without a Lid is to be made from 12 m^2 of Cardboard. Find the Maximum Volume of such a Box.

41:15 Absolute Maximum and Minimum Values; The Extreme Value Theorem in One Dimension.

42:15 Absolute Maximum and Minimum Values; The Extreme Value Theorem in Two Dimensions.

44:55 Extreme Value Theorem for Functions of Two Variables.

46:23 Find the Absolute Maximum and Minimum Values of the Function:

 f ( x, y ) = x^2 - 2xy + 2y On the Rectangle: D { (x, y) / x Belongs to [ 0, 3 ] and y belongs to [ 0, 2 ]}.