EXAM 3 Section XXX
April 6, 2005
NAME:
Make sure to read the question carefully and answer the question that is asked. Show ALL relevant work so
that partial credit may be given and indicate where the solution is. Lack of sufficient work may result in a
loss of credit, even if a correct answer is given.
Good luck!!
“On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho
rized assistance on this work.”
YOUR SIGNATURE:
1.
Partial Derivatives
(7 points)
Find all the first partial derivatives of the following functions.
(a)
f
(
x,y
) =
x
2
y
+
xy
2
Solution:
f
x
(
x,y
) = 2
xy
+
y
2
f
y
(
x,y
) =
x
2
+ 2
xy
(b)
g
(
x,y
) =
e
x
2
+
e
xy
Solution:
g
x
(
x,y
) = 2
xe
x
2
+
ye
xy
g
y
(
x,y
) =
xe
xy
(c)
h
(
x,y,z
) =
xy
2
+
yz
2
+
xyz
Solution:
h
x
(
x,y,z
) =
y
2
+
yz
h
y
(
x,y,z
) = 2
xy
+
z
2
+
xz
h
z
(
x,y,z
) = 2
yz
+
xy
1
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2.
Absolute Extrema
(8 points)
Find the absolute minimum value and the absolute maximum value, if any, for the function
h
(
t
) =
t
3

6
t
2
on the interval[

1
,
2]
.
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 Spring '08
 JOHANSON
 Calculus, Critical Point, Derivative

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