B. Sketch a graph of function g given that it has the following properties: - g(-2) = 6; - g(1) = 2; - g(3) = 4; - g′ (1) = g′ (3) = 0; For every satisfying the inequality |x − 2| > 1, the value of g′ (x) is negative; For every a satisfying the inequality |x − 2| < 1, the value of g′ (x) is positive; For every x satisfying either |x + 1| < 1 or x > 2, the value of g" (x) is negative; For every x satisfying either |x − 1| < 1 or x < -2, the value of g" (x) is positive.
B. Sketch a graph of function g given that it has the following properties: - g(-2) = 6; - g(1) = 2; - g(3) = 4; - g′ (1) = g′ (3) = 0; For every satisfying the inequality |x − 2| > 1, the value of g′ (x) is negative; For every a satisfying the inequality |x − 2| < 1, the value of g′ (x) is positive; For every x satisfying either |x + 1| < 1 or x > 2, the value of g" (x) is negative; For every x satisfying either |x − 1| < 1 or x < -2, the value of g" (x) is positive.
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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Transcribed Image Text:B. Sketch a graph of function g given that it has the following properties:
- g(−2) = 6;
- g(1) = 2;
- g(3) = 4;
- g′(1) = g′ (3) = 0;
For every a satisfying the inequality |x − 2| > 1, the value of g′ (x) is negative;
For every a satisfying the inequality |x − 2| < 1, the value of g'(x) is positive;
For every x satisfying either |ï +1| < 1 or x > 2, the value of g'(x) is negative;
For every satisfying either x − 1| < 1 or x < −2, the value of g" (x) is positive.
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