Question

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 } .

Absolute maximum value =

Absolute minimum value =

Answer #1

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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)

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).

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 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 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)

Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
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List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

Find the absolute maximum value of the function
f(x,y)=x2-4xy+y3+4y on the triangular region
with vertices (-1,-1), (7,-1) and (7,7).

Find the absolute maximum and minimum values of f on
the set D.
f(x, y) =
4x + 6y −
x2 − y2 +
3,
D = {(x,
y) | 0 ≤ x ≤ 4, 0 ≤
y ≤ 5}
absolute maximum value
absolute minimum value

Find the absolute maximum value and absolute minimum value of
f(x,y) = x2 +2y2−2x−4y+1 on the region D = {(x,y) ∈ R2 : 0 ≤ x ≤
2,|y−1.5|≤ 1.5}

1. Find the absolute maximum value and the absolute minimum
value, if any, of the function. (If an answer does not exist, enter
DNE.)
g(x) =
−x2 + 4x + 9
maximum =
minimum=
2. Find the absolute maximum value and the absolute minimum
value, if any, of the function. (If an answer does not exist, enter
DNE.)
f(x) = x2 − x − 3 on [0, 3]
3.
Find the absolute maximum value and the absolute minimum value,
if...

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