This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 16 — Related Rates Recall our problem of a ladder sliding away from a wall. Examine the pictures below. If we freeze the picture at a particular time t , then the values of x and y can be measured and recorded; therefore x and y are both functions of time t , say x ( t ) and y ( t ) . By Pythagorean Theorem, we have the following identity for all t during which the ladder is in motion: and hence by chain rule, We did this without having to find formulas for x ( t ) and y ( t ) ...knowing that those functions satisfied an identity allowed us to find a relationship between their rates of change dy dt and dx dt . Suppose, in our ladder problem, that we know the ladder is sliding out from the wall at a constant 2 m/s. At what rate is y changing when the ladder is 6 feet from the wall? 8 feet from the wall? Suppose the ladder does not slide out at a constant rate, but we use a device to measure that it is sliding out at 2 m/s at the instant it is 6 feet from the wall....
View
Full
Document
This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus

Click to edit the document details