Question

Find the maximum and minimum of the function f (x, y) = 6x − 2y subject to the constraint . 3x^2 + y ^2 = 4

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

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.

Find the maximum and minimum values of the function
f(x,y,z)=x+2y subject to the constraints y^2+z^2=100 and x+y+z=5. I
have: The maximum value is ____, occurring at (___, 5sqrt2,
-5sqrt2). The minimum value is ____, occurring at (___, -5sqrt2,
5sqrt2). The x-value of both of these is NOT 1. The maximum and
minimum are NOT 1+10sqrt2 and 1-10sqrt2, or my homework program is
wrong.

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.

Find the maximum and minimum values of the function
f(x,y,z)=3x−y−3 subject to the constraints x^2+2z^2=324 and
x+y−z=−6 . Maximum value is , occuring at ( , , ). Minimum value is
, occuring at ( , , ).

(9)
(a)Find the double integral of the function f (x, y) = x + 2y
over the region in the plane bounded by the lines x = 0, y = x, and
y = 3 − 2x.
(b)Find the maximum and minimum values of 2x − 6y + 5 subject to
the constraint x^2 + 3(y^2) = 1.
(c)Consider the function f(x,y) = x^2 + xy. Find the directional
derivative of f at the point (−1, 3) in the direction...

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

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.

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