Question

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum.

f(x,y)= 3x^2+4y^2-4xy; x+y=11

thwew is a (minimum/maximum) value of --- located at (x,y)=---

Answer #1

Find the extremum of f(x,y) subject to the given constraint,
and state whether it is a maximum or a minimum. f(x,y)=4y^2-12x^2;
2x+y=8.

Find the extremum of f(x,y) subject to the given constraint,
and state whether it is a maximum or a
minimum.f(x,y,z)=x^2+y^2+z^2;2x+4y-4z=9.

Find the extremum of f(x,y) subject to the given constraint,
and state whether it is a maximum or a
minimum.f(x,y,z)=x^2+y^2+z^2;x+3y-4z=26.

Use the method of Lagrange multipliers to find the maximum value
of f subject to the given constraint. f(x,y)=−3x^2−4y^2+4xy,
subject to 3x+4y+528=0

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 the method of Lagrange Multipliers to find the extreme
value(s) of f(x, y) = 3x + 2y subject to the constraint y = 3x ^2 .
Identify the extremum/extrema as maximum or minimum.

Find the indicated maximum or minimum value of f subject to the
given constraint.
Minimum: f(x,y)=2 x^2 + y ^2 + 2 xy + 3 x + 2 y
; y^2 = x + 1
The minimum value is -------------.
(Type an integer or a simplified fraction.)

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

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.

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.

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