Homework 10/10
Fall 2011
Goals:
•
Work Type I problems in which some or all functions are implicit.
•
Be able to recognize what role a letter plays in a given problem. Sometimes it’s a constant;
sometimes it’s an input variable; sometimes it’s an unknown or implicit function.
Warm Up:
1. Suppose that
x
2
+
y
2
= 100. Find
dy
dx
at the location
x
= 5,
y
=

5
√
3.
2. Suppose that
x
2
+
y
2
= 100. In this problem:
•
y
measures the height of an object in feet
•
x
measures the position of a second object in feet.
•
t
is time in seconds.
•
dx
dt
=

2 ft/s.
Find
dy
dt
when
x
= 5
√
3 feet and
y
= 5 feet.
Exercises:
1. Suppose that
x
2
=
y
3
. In this problem
•
y
is measured in feet and is a function of time,
t
.
•
x
is measured in feet and is a function of time,
t
.
•
t
is measured in seconds.
Find
dy
dt
when
x
= 8 feet,
y
= 4, and
dx
dt
=

3 ft/s.
2. Suppose that
x
2
+
y
2
= 169. In this problem
•
x
and
y
measure the positions of two moving objects, both measured in miles.
•
t
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 Fall '08
 STAFF
 Math, Calculus

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