Question

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.

Answer #1

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.

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 locate the maximum of f(x,y,z) =
2x^2 - 2y + z^2 subject to the constraint x^2 + y^2 + z^2 = 1

Use Lagrange multipliers to find the extremal values of
f(x,y,z)=2x+2y+z subject to the
constraint
x2+y2+z2=9.

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

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 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 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.

Find the maximum and minimum values of f(x,y,z)=2x-2y-z on the
closed and bounded set 4x^2+2y^2+z^2 ≤ 1

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