Question

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.

Answer #1

The function f(x,y,z)= 4x+z^2 has an absolute maximum and
minimum values subject to the constraint of 2x^2+2y^2+3z^2=50. Use
Lagrange multipliers to find these values.

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)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.

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.

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 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 Lagrange multipliers to find the maximum and minimum values
of f(x,y)=x2+5y
subject to the constraint x2-y2=3 , if
such values exist.
Maximum =
Minimum

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 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 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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