Question

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

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 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 maximum and minimum values of f(x,y,z)=2x-2y-z on the
closed and bounded set 4x^2+2y^2+z^2 ≤ 1

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 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 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

find the absolute maximum and absolute minimum values of f on the
given interval
f(x) = x^4-2x^2+1 [-2,3]

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 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}

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