Question

Find the indicated maximum or minimum value of f subject to the given constraint. Maximum: f(x,y,z) = (x2)(y2)(z2); x2 + y2 + z2 = 6

Answer #1

Find the indicated maximum or minimum value of f subject to the
given constraint. Minimum : f(x,y)=
2x2+y2+2xy+3x+2y; y^2=x+1

Find the maximum and minimum values of the function
f(x,y,z)=x2y2z2 subject to the constraint x2+y2+z2=361.
Maximum value is:........... , occuring at ...............
points (positive integer or "infinitely many"). Minimum value is
........................ , occuring at ..................... points
(positive integer or "infinitely many").
Please fill in the blanks

Use the method of Lagrange Multipliers to find the maximum
value:
f(x,y,z) = x2y2z2 subject to
the constraint x2+y2+z2=1 no
decimals permitted

Use Lagrange Multiplers to find the minimum of the function
subject to the given constraint(s).
f(x,y,z,t)=7x+7y+7z+7t,
7(x2+y2+z2+t2)=8

Find the maximum and minimum values of the following function,
subject to the given constraint. Maximize and minimize the function
f(x, y) = xy2 subject to the constraint x2 + y2 = 1.
maximum of ____at (x, y) = (____,_____)
minimum of _____ at (x, y) = (_____,____)

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 the method of Lagrange multipliers to find the maximum and
minimum values of F(x,y,z) = 5x+3y+4z, subject to the constraint
G(x,y,z) = x2+y2+z2 = 25. Note the
constraint is a sphere of radius 5, while the level surfaces for F
are planes. Sketch a graph showing the solution to this problem
occurs where two of these planes are tangent to the sphere.

Find the minimum of f(x, y, z) = x2 + y2 +
z2 subject to the two constraints x + y + z = 1 and 4x +
5y + 6z = 10

Find the minimum and maximum values of the function
f(x,y)=x2+y2f(x,y)=x2+y2 subject to the given constraint
x4+y4=2x4+y4=2.
(The minimum is not not zero, DNE, or NONE, I have tried all of
those)

Find the minimum value of the function f(x,y)=2x+y, subject to
the constraint x2+y2=5.

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