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Find the domain of f and the intercepts of the graph of f.

Find the domain of f and the intercepts of the graph of f.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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r(9 – x2) (3 – 2)2 6x (r2 + 9) 1. Given f(r) = with f'(x) = and f"(x) = 3 - 12 (3 – 12)3 (a) Find the domain of f and the intercepts of the graph of f. (b) Verify that the lines r = v3, z = -v3 and y = -r are linear asymptotes of the graph of f. (c) Identify the critical numbers and the possible points of inflections of the graph of f. (d) Make a table that shows the intervals where f is increasing or decreasing, and where the graph of f is concave up or concave down. Specify in the table all relative extremum points and possible points of inflections of the graph of f. (e) Sketch the graph of f. Reminder: Emphasize concavity in your graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with their equations. 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that there are two distinct real numbers r and r2 such that f'(r1) = -f'(x2).
Transcribed Image Text:r(9 – x2) (3 – 2)2 6x (r2 + 9) 1. Given f(r) = with f'(x) = and f"(x) = 3 - 12 (3 – 12)3 (a) Find the domain of f and the intercepts of the graph of f. (b) Verify that the lines r = v3, z = -v3 and y = -r are linear asymptotes of the graph of f. (c) Identify the critical numbers and the possible points of inflections of the graph of f. (d) Make a table that shows the intervals where f is increasing or decreasing, and where the graph of f is concave up or concave down. Specify in the table all relative extremum points and possible points of inflections of the graph of f. (e) Sketch the graph of f. Reminder: Emphasize concavity in your graph of f. Plot the intercepts, relative extremum points, and points of inflection, and label them with their coordinates. Draw the linear asymptotes and label them with their equations. 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that there are two distinct real numbers r and r2 such that f'(r1) = -f'(x2).
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