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Lecture 20: Related Rates
(Chapter 3, Section 20)
Consider the following example:
A point is moving along the graph of the function
y
=
1
1 +
x
2
so that the velocity in the
x
direction as
it passes the point (
¡
2
;
1
5
) is 2 cm/min. What is the
velocity in the
y
direction at this time?
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Related Rates
allows us to ﬂnd the rate of change
of one quantity in terms of the rate of change of a
related quantity.
To solve a related rates problem:
1) Identify the desired rate of change; assign variables
to all related quantities. Determine what rate(s) and
information are given. Draw a sketch if possible.
2) Write an equation (mathematical
model
) relating
the variables involved.
3) Diﬁerentiate the equation implicitly with respect
to time.
4) Substitute known values and solve for the desired
rate of change.
ex.
A spherical balloon is in±ated with gas at a rate
of 8
…
cubic ft/min. How fast is the radius changing
when the volume is 36
…
cubic ft?
How fast is the surface area changing at that same
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Geometry

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