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Math 20C Spring 1995
Exam 2
Helton
Give explanations which tell us clearly every step of what you are doing.
Let
F
(
x, y, z
)=(
x
2
+
y
2
x
2
)+
x
+ 100. Suppose the graph of
F
represents a shiny smooth
hill.
1.
What are the partial derivatives of
F
with respect to
x
and
y
.
2.
What is the gradient?
Suppose you are standing over the point
x
=1
,y
= 2 on the hill.
3.
If you drop a marble, in which direction will it start to roll? You only need to specify
the direction in the
x, y
plane which it will take.
4.
What is the slope of the hill in the direction of the vector (2
,
4)?
5.
Suppose you lay a ruler (1 foot) down on the hill pointing in the northeast direction
with one tip at your feet. Approximately how much higher is the other tip? Here we
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 Spring '08
 Helton
 Derivative

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