Question

Find the relative maximum value of f(x,y,z)=xyz^{2},
subject to the constraint x+y+5z=6

The Relative Maximum value is f(_,_,_)=_

Answer #1

Find the relative maximum value of
f(x,y)=x2-9y2, subject to the constraint
x-y=24
The relative maximum value is f(_,_) = _

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 relative minimum value of
f(x,y)=4x2 +4y2 -2xy,
subject to the constraint
x+y=4.
The value is f(_,_)= _

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

Use the method of Lagrange Multipliers to find the maximum
value:
f(x,y,z) = x2y2z2 subject to
the constraint x2+y2+z2=1 no
decimals permitted

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 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

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.

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.

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