Question

1. Use the method of Lagrange multipliers to find the maximize

of the function f (x, y) = 25-x^2-y^2 subject to the constraint x + y =-1

2. Use the method of Lagrange multipliers to find the minimum

of the function f (x, y) = y^2+6x subject to the constraint y-2x= 0

Answer #1

Use the method of Lagrange Multipliers to find the maximum value
of the function f(x,y)= x^3y^2 subject to the constraint
x^2+y^2=10.

Use Lagrange multipliers to find both the maximum and minimum of
the function f(x, y) = 3x + 4y subject to the constraint that the
point be on the circle x 2 + y 2 = 100.

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

use the method of Lagrange multipliers to find the absolute
maximum and minimum values of the function subject to the given
constraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2≤9 and
y≥0

Use Lagrange multipliers to find all relative extrema of the
function subject to the given constraint.
f(x,y)=x^2+2y^3
constraint: 2x+y^2-8=0

Use Lagrange multipliers to find the indicated extrema, assuming
that x and y are positive.
Maximize f(x, y) = 2x + 3xy + y
Constraint: x + 2y = 33

Use the method of Lagrange multipliers to find the maximum value
of f subject to the given constraint. f(x,y)=−3x^2−4y^2+4xy,
subject to 3x+4y+528=0

Use the method of Lagrange Multipliers to find the extreme
value(s) of f(x, y) = 3x + 2y subject to the constraint y = 3x ^2 .
Identify the extremum/extrema as maximum or minimum.

Use the Lagrange Multipliers method to find the maximum and
minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2
+ z2 = 4.

Calculus III. Please show all work and mark the
answer(s)!
1) Use Lagrange multipliers to find the maximum and minimum
values of the function f(x, y) = x^2 + y^2 subject to the
constraint xy = 1.
2) Use Lagrange Multipliers to find the point on the curve 2x +
3y = 6 that is closest to the origin. Hint: let f(x, y) be the
distance squared from the origin to the point (x, y), then find the
minimum of...

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