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Get Full Access to Calculus - 8 Edition - Chapter 10 - Problem 4
Get Full Access to Calculus - 8 Edition - Chapter 10 - Problem 4

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# Four bugs are placed at the four corners of a square with

ISBN: 9781285740621 127

## Solution for problem 4 Chapter 10

Calculus | 8th Edition

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Calculus | 8th Edition

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Problem 4

Four bugs are placed at the four corners of a square with side length a. The bugs crawl counterclockwise at the same speed and each bug crawls directly toward the next bug at all times. They approach the center of the square along spiral paths. (a) Find the polar equation of a bugs path assuming the pole is at the center of the square. (Use the fact that the line joining one bug to the next is tangent to the bugs path.) (b) Find the distance traveled by a bug by the time it meets the other bugs at the center.

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Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local extremum (c), then f’(c) = 0. It is impossible that f is not differentiable at a local extremum. Definition: f has a critical point at x if f ’(x) = 0 or f ’(x) DNE. Coordinates for local extremum will be critical points. We see that, if f ‘(x) is negative on an interval I, then f is decreasing on I. If f ‘(x) is positive on an interval I, then f is

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