Respuesta :
The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.
The absolute maximum point is a point where the function obtains its greatest possible value.
And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.
Given equation is, f(x,y) = 3 + xy - x - 2y
we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).
f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3
f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2
f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1
Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).
An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.
Given question is incomplete. Complete question is:
find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).
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