Question

Find the maximum and minimum values of
x^{2}+y^{2} subject to the constraint
x^{2}-8x+y^{2}-4y=0.

The minimum value of x^{2}+y^{2} is (?)

The maximum value of x^{2}+y^{2} is (?)

Answer #1

Find the maximum and minimum values of
x2+y2 subject to the constraint
x2-8x+y2-4y=0
minimum value of x2+y2
maximum value of x2+y2

Find the locations of the maximum and minimum values for
f(x)=6x+9y+1 subject to the constraint x2+y2−4=0 Enter your answer
as a list of points separated by commas

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

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)=81x2+y2f(x,y)=81x2+y2 subject to the constraint
4x2+y2=94x2+y2=9.

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