4748. Laplaces equation Verify that the following functions satisfy Laplaces equation 02u 0x2 + 02u 0y2 = 0. u1x, y2 = ln 1x2 + y22
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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
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs
The full step-by-step solution to problem: 48 from chapter: 12 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. The answer to “4748. Laplaces equation Verify that the following functions satisfy Laplaces equation 02u 0x2 + 02u 0y2 = 0. u1x, y2 = ln 1x2 + y22” is broken down into a number of easy to follow steps, and 25 words. Since the solution to 48 from 12 chapter was answered, more than 237 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.