Question

Find the absolute maximum of f(x, y) = - 2y/(x^2 + y^2 + 1) on the region R = {(x, y) such that x^2 + y^2 <= 4}

Express the answer as an ordered triple.

Answer #1

Find the absolute minimum of f(x,y)=x^2−y^2−x on the region
R={(x,y)|3≤x≤5,2≤y≤4}. Express the answer as an ordered triple.

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 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

1. Find the absolute maximum of f(x,y)=x^2+2y^2+4y-2 on the disk
x^2+y^2<=4
2. Let E be the solid bounded by x^2+y^2=4, y+z=2, and z=0. What
is the volume of the solid E?

Find the absolute maximum and minimum values of the function f
(x, y) = x^2 xy+on the region R bounded by the graphs of y = x^2
and y = x+ 2

Find the absolute maximum and minimum vaues of f on the set
D.
f(x,y)=x^2 + y^2 + x^2y +4, D={ (x,y)| -1 less than or equal to
x less than or equal to 1, -1 less than or equal to y ess than or
equal to 1}

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).

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

Find the absolute maximum and minimum of f(x,y)=5x+5y with the
domain x^2+y^2 less than or equal to 2^2
Suppose that f(x,y) = x^2−xy+y^2−2x+2y with
D={(x,y)∣0≤y≤x≤2}
The critical point of f(x,y)restricted to the boundary of D,
not at a corner point, is at (a,b)(. Then a=
and b=
Absolute minimum of f(x,y)
is
and absolute maximum is .

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).

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