Multivariable Calculus Quiz
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OPTIMIZATION IN SEVERAL VARIABLES
Question 1
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Find the maximum value of the function
f
(
x
,
y
,
z
)
=
x
2
+
y
2
+
z
2
f(x, y, z) = x^2 + y^2 + z^2
f
(
x
,
y
,
z
)
=
x
2
+
y
2
+
z
2
on the curve of intersection of the cylinder
x
2
+
y
2
=
1
x^2 + y^2 = 1
x
2
+
y
2
=
1
and the plane
x
+
y
+
z
=
1
x + y + z = 1
x
+
y
+
z
=
1
.
A
1
1
1
B
4
−
2
2
4 - 2\sqrt{2}
4
−
2
2
C
4
+
2
2
4 + 2\sqrt{2}
4
+
2
2
D
1
+
2
1 + \sqrt{2}
1
+
2
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