Question

Find the absolute maximum and minimum values of *f* on
the set *D*.

* f*(

* D* = {(

absolute maximum value | |

absolute minimum value |

Answer #1

Find the absolute maximum and minimum values of f on
the set D.
f(x, y) =
4x + 6y −
x2 − y2 +
8,
D = {(x,
y) | 0 ≤ x ≤ 4, 0 ≤
y ≤ 5}
Find the absolute maximum and minimum values of f on
the set D.
f(x, y) = 2x3 + y4 +
2, D = {(x, y) | x2 +
y2 ≤ 1}

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) =
4x + 6y −
x2 − y2 +
2,
D = {(x,
y) | 0 ≤ x ≤ 4, 0 ≤
y ≤ 5}

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 and minimum values of f on the set
D.
f(x,y)=2x^3 +y^4 +2, D== {(x,y)|?^2 + ?^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 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 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 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

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