Question

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}

Answer #1

The local maximum value of the function f(x,y) = x2 + 2y2 − 2xy
− 4y + 3 is
(A) −6 (B) 4 (C) −1 (D) 1 (E) 3 (F) none of (A) - (E)

Find the absolute maximum value and the absolute minimum value
of the function f(x,y)=(1+x2)(1−y2) on the disk
D={(x,y) | x2+y2⩽1}

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

Find the absolute maximum and minimum values of f on
the set D.
f(x, y) =
x2 + y2 +
x2y + 6,
D = {(x,
y) | |x| ≤ 1,
|y| ≤ 1}
absolute maximum value
absolute minimum value

The function f(x,y)=4x-4y has an absolute maximum value and
absolute minimum value subject to the constraint x^2-xy+y^2=9. Use
Lagrange multipliers to find these values.

Find the absolute maximum and minimum of the function
f(x,y,z)=x^2 −2x+y^2 −4y+z^2 +4z
on the ball of radius 4 centered at the origin (i.e., x^2 + y^2
+ z^2 ≤ 16). Lay out your work neatly and clearly show your
procedure.

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