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,z)=x^2+y^2+z^2;x+3y-4z=26.

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,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)=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)= 3x^2+4y^2-4xy; x+y=11
thwew is a (minimum/maximum) value of --- located at
(x,y)=---

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 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.)

Use the method of Lagrange multipliers to find the maximum value
of f(x,y) = xy subject to the constraint x^2=y^2=7 (you may assume
that the extremum exists)

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 relative maximum value of f(x,y,z)=xyz2,
subject to the constraint x+y+5z=6
The Relative Maximum value is f(_,_,_)=_

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 value of the function f(x,y) = 2x - 5(y^2)
subject to the constraint (x^2)+5(y^2) = 25.

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