Absolute Minimum and Maximum Value of a Function on a Set

Find the absolute maximum and minimum values of f on the set D.
28. f(x, y) = 3 + xy ? x ? 2y, D is the closed triangular region with vertices (1, 0), (5, 0), and (1, 4)
24. Use Lagrange multipliers to prove that the triangle with maximum area that has a given perimeter p is equilateral.

28.
From the matrix of 2nd derivatives of f(x,y) we see that is does not produce a sign-defined quadratic form, therefore f(x,y) has no local extrema anywhere, and so its absolute extrema in a bounded region ar on the boundaries of the region.
In this case these are the sides of the triangle.
The side (1,0)-(5,0) has y = 0 and so f = 3 - x on it, with extrema at the vertices (1,0) and (5,0), equal to 2 and -2, respectively.
The side (1,0)-(1,4) has x = 1 and so f = 2 - ...

Solution Summary

The Absolute Minimum and Maximum Values of a Function on a Set are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... Computing the value of f at each of these critical points (I ... This solution provides two examples of finding absolute maximum and minimum values of a ...

... 5 .5 ⇒ C ( − 5 ,0 ) Now we can compute the value of f(x ... y , z ) | C = 150 So, we conclude that the absolute maximum is 150 and the absolute minimum is -5 ...

... 37 Minimizing the Maximum of Absolute Values . . ... The solution of the minimum problem is obtained by letting ... The solution of the maximum problem is obtained by ...

... With its mission of delivering maximum value to its customers, the ... in its vision and with absolute devotion, honesty ... the given task in the minimum time with ...

... 1-30 Cell References Relative addressing: B5, G13 Absolute addressing: $B ... 50, 70, 90} Range difference between the maximum and minimum observations Same ...

... or collection of cells, just use the MAX formula. ... red because they didn't achieve a minimum sales amount ... cells, you would want to place an absolute reference on ...

... Cardinal utility functions = the absolute difference between ...function, which expresses the maximum attainable utility ...function which is the minimum cost of ...

... 4 Find the slope of the Tangent line to the given curve at the given value of x. Find the equation ... So, the absolute maximum is 1, and absolute minimum is -80. ...

... not bound by same facilities sharing requirements as firms ...Absolute value of point elasticity of demand is less ... We see that maximum revenue that company can ...

... Although it is not an absolute requirement, for maximum credit on ... If this turns out to be the maximum for all sales ... The minimum valid initial base year is 2005 ...