Consider the following function. f(x, y) = x² + y² + x²y+9 Find the following derivatives. f(x, y) = 2x+ 2xy

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Only find minm and maxm
Consider the following function.
Find the following derivatives.
f(x, y) = 2x + 2xy
fy(x, y) = 2y + x²
f(x, y) = x² + y² + x²y+9
Find the critical point.
(x, y) =
0.0
Find the value off at this critical point.
9
Find the minimum and maximum of fon each segment of the boundary.
x = 1
y = -1 DNE
y=1
x = -1
minimum
10
DNE
X
x
absolute maximum value
absolute minimum value
x
X
1
1
maximum
x
x
x
x
Find the absolute maximum and minimum values of f on the set D.
D = {(x, y) | Ix ≤ 1, 1y| ≤ 1}
12
9
Transcribed Image Text:Consider the following function. Find the following derivatives. f(x, y) = 2x + 2xy fy(x, y) = 2y + x² f(x, y) = x² + y² + x²y+9 Find the critical point. (x, y) = 0.0 Find the value off at this critical point. 9 Find the minimum and maximum of fon each segment of the boundary. x = 1 y = -1 DNE y=1 x = -1 minimum 10 DNE X x absolute maximum value absolute minimum value x X 1 1 maximum x x x x Find the absolute maximum and minimum values of f on the set D. D = {(x, y) | Ix ≤ 1, 1y| ≤ 1} 12 9
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