Question

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

Answer #1

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

Find the minimum and maximum values of the function f(x,y)=x2+y2
subject to the constraint x4+y4=2592 Use the Lagrange equations

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

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 the method of Lagrange multipliers to find the minimum value
of the function
f(x,y,z)=x2+y2+z2
subject to the constraints x+y=10 and 2y−z=3.

Find the maximum and the minimum values of f(x,y,z)=7x-9y+6z on
the sphere x2+y2+z2=166. The
maximum value is (?). The minimum value is (?).

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)

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

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) = (_____,____)

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

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