Finding Maximum and Minimum Values (a) Let f ( x , y ) = x − y and g ( x , y ) = x 2 + y 2 = 4 . Graph various level curves of f ad the constraint g in the x y -plane. Use the graph to determine the maximum value of f subject to the constraint g = 4 . Then verify your answer using Lagrange multipliers. (b) Let f ( x , y ) = x − y and g ( x , y ) = x 2 + y 2 = 0 . Find the maximum and minimum values of f subject to the constraint g = 0 . Does the Method of Lagrange Multipliers work in this case? Explain.
Finding Maximum and Minimum Values (a) Let f ( x , y ) = x − y and g ( x , y ) = x 2 + y 2 = 4 . Graph various level curves of f ad the constraint g in the x y -plane. Use the graph to determine the maximum value of f subject to the constraint g = 4 . Then verify your answer using Lagrange multipliers. (b) Let f ( x , y ) = x − y and g ( x , y ) = x 2 + y 2 = 0 . Find the maximum and minimum values of f subject to the constraint g = 0 . Does the Method of Lagrange Multipliers work in this case? Explain.
Solution Summary: The author explains how to calculate f(x,y) = x-y and g (x), based on Lagrange's Theorem.
(a) Let
f
(
x
,
y
)
=
x
−
y
and
g
(
x
,
y
)
=
x
2
+
y
2
=
4
. Graph various level curves of
f
ad the constraint
g
in the
x
y
-plane. Use the graph to determine the maximum value of
f
subject to the constraint
g
=
4
. Then verify your answer using Lagrange multipliers.
(b) Let
f
(
x
,
y
)
=
x
−
y
and
g
(
x
,
y
)
=
x
2
+
y
2
=
0
. Find the maximum and minimum values of
f
subject to the constraint
g
=
0
. Does the Method of Lagrange Multipliers work in this case? Explain.
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y) = x2 − y2; x2 + y2 = 49
maximum value
?
minimum value
?
Please Help find Maximum and minimum value.
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y) = x2 − y2; x2 + y2 = 49
Maximum Value=?
Minimum Value=?
Thank You
Use the method of Lagrange multipliers to maximize the function subject to the given constraint.
Maximize the function
f(x, y) = 16 − x2 − y2
subject to the constraint
x + y − 6 = 0.
maximum of______at (x, y) =
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