# 1. Explain why, at a point that maximizes or minimizes  subject to a constraint g 1 x , y 2 = 0,…

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1. Explain why, at
a point that maximizes or minimizes  subject
to a constraint g1x, y2
=
0,
the gradient of  is parallel to the gradient of g. Use
a diagram.

2. Describe the
steps used to find the absolute maximum value and absolute minimum value of a
differentiable function on a circle centered at the origin of the xy-plane.

3. For functions 1x, y2
=
x
+
4y and g1x, y2
=
x2 +
y2 –
1,
write the Lagrange multiplier conditions that must be satisfied by

a point that maximizes or minimizes  subject
to the constraint g1x, y2
=
0.

4. For functions 1x, y, z2
=
xyz
and
g1x, y, z2
View complete question »

1. Explain why, at
a point that maximizes or minimizes  subject
to a constraint g1x, y2
=
0,
the gradient of  is parallel to the gradient of g. Use
a diagram.

2. Describe the
steps used to find the absolute maximum value and absolute minimum value of a
differentiable function on a circle centered at the origin of the xy-plane.

3. For functions 1x, y2
=
x
+
4y and g1x, y2
=
x2 +
y2 –
1,
write the Lagrange multiplier conditions that must be satisfied by

a point that maximizes or minimizes  subject
to the constraint g1x, y2
=
0.

4. For functions 1x, y, z2
=
xyz
and
g1x, y, z2
=
x2 +
2y2 +
3z2 –
1,
write the Lagrange multiplier conditions that must be satisfied by a point that
maximizes or minimizes  subject to the
constraint g1x, y2
=
0.

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