Question

Determine the absolute minimum and maximum values of the function f(x, y) = 2x^2 −2xy +y^2 −2y + 7 on the closed triangular region with vertices (0, 0), (3, 0), and (0, 3).

Answer #1

Find the absolute maximum and absolute minimum values of f(x,y)
= x^2 + 2y^2 − 2x + 2 on the closed disk D: x^2 + y^2 ≤ 4.
Answer: absolute min: f(1, 0) = 1; absolute max: f(−1, ± √3) =
11

Find the absolute maximum and minimum values of
f(x,y)=2x^2+y^2-xy^2 on the triangular region shown with vertices
(0,0), (0,4) and (4,4).

Find the absolute maximum value and the absolute minimum value
of the function f ( x , y ) = x 2 y 2 + 3 y on the set D defined as
the closed triangular region with vertices ( 0 , 0 ), ( 1 , 0 ),
and ( 1 , 1 ), that is, the set D = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y
≤ x }...

Find the absolute maximum and minimum values of f(x, y) = 4xy +
x^2 on the
triangular region D in the xy-plane with vertices (4, 0), (0, 3),
and (2, 4).

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

find the absolute maximum value and absolute minimum values of
the function f(x,y)4xy^2-x^2y^2-xy^3 on the set D, where D is the
closed trianglar region in the xy-plane with certices
(0,0)(0,6)(6,)0

Find the absolute min and max values of the function
f(x, y) =x + y− x^2y on the closed triangular region with
vertices (0,0), (3,0), and (0,3).

Calculate the following: absolute maximum, absolute minimum
values of f(x, y) = 2x^2y on -> 2x^2+y^2=6

2. Find the absolute maximum and minimum values of the function
f(x, y) = 2x^3 + y^4 on the unit disk.

Find the absolute maximum and minimum values of f(x,y)=4xy+x^2
on the triangular region D in the xy plane with the vertices (4,0)
(0,3) and (2,4)

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