Question

The function

f(x,y)equals=8 x squared plus y squared

has an absolute maximum value and absolute minimum value subject to the constraint

x squared plus 7 y plus y squared=44.

Use Lagrange multipliers to find these values.

Answer #1

The function f(x,y)equals2 x squared plus y squared has an
absolute maximum value and absolute minimum value subject to the
constraint x squared plus 4 y plus y squaredequals32. Use Lagrange
multipliers to find these values.

The function f(x,y)=4x-4y has an absolute maximum value and
absolute minimum value subject to the constraint x^2-xy+y^2=9. Use
Lagrange multipliers to find these values.

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.

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) = 10x + 2y; x2 + y2 = 26

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.

Use Lagrange multipliers to find the maximum and minimum values
of f(x,y)=4x3+y2 subject to the constraint 2x2+y2=1 also, find the
points at which these extreme values occur.

Use Lagrange multipliers to find the maximum and minimum values
of
f(x,y)=xy
subject to the constraint 25x^2+y^2=200
if such values exist.
Enter the exact answers. Which is global maximum/global minimum?
Enter NA in the appropriate answer area if these do not apply.

Use Lagrange multipliers to find the maximum value of the
function f(x,y) = xy given the constraint x+y=10

f(x,y)=xy ; 4x^2+y^2=8
Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.

Use the method of Lagrange multipliers to find the maximum value
of f(x,y) = xy subject to the constraint x^2=y^2=7 (you may assume
that the extremum exists)

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