Question

Find the absolute max and min for f(x,y) = (x-3)^2+y^2 on D={(x,y):0 ≤ x ≤ 4 , x^2 ≤ y ≤ 4x}.

Answer #1

. Find the absolute max and min of the following function f(x,
y) = x^2 + 2xy − y^2 − 4x, 0 ≤ x ≤ 2, 0 ≤ y ≤ 2.

find absolute max and min
f(x)= ln(x^3 -2x^2 +x) [1/4, 3/4]

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 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).

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 max and absolute min of f(x)= x3 -x
-1 on the interval [-1, 2]

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 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 extrema (absolute max/min) of ?(?, ?) = ?? − ?
− 2? + 8 on the triangular region ? with vertices (0,0), (4,0), ???
(0,4). Draw the region and call the boundary on the x-axis ?1 (?,
?), the boundary on the y-axis ?2 (?, ?), and the boundary on the
diagonal of the triangle ?3 (?, ?). Note: Re-write each boundary as
a function of one-variable.

what is the absolute max and min
f(x) = x + e^-2x
[-1 , 3]

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