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2. In each part below, sketch the graph of a function g that satisfies the given conditions if possible. If it is not possible, indicate this and do not give a sketch. (a) g(0) = 1, g'(0) = 0, g(2) = 0, g'(2) = 1 g is continuous everywhere. (c) g is differentiable at x = 2 but g is not continuous at x = 2.

2. In each part below, sketch the graph of a function g that satisfies the given conditions if possible. If it is not possible, indicate this and do not give a sketch. (a) g(0) = 1, g'(0) = 0, g(2) = 0, g'(2) = 1 g is continuous everywhere. (c) g is differentiable at x = 2 but g is not continuous at x = 2.

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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2. In each part below, sketch the graph of a function g that satisfies the given conditions if possible. If it is not possible, indicate this and do not give a sketch. (a) g(0) = 1, g'(0) = 0, g(2) = 0, g'(2) = 1 is continuous everywhere. (b) y = g(x) is increasing but at a decreasing rate. (c) g is differentiable at x = 2 but g is not continuous at x = 2. (d) lim g(x) and lim g(x) exist x→2+ x→2¯ but lim g(x) does not exist. x→2
Transcribed Image Text:2. In each part below, sketch the graph of a function g that satisfies the given conditions if possible. If it is not possible, indicate this and do not give a sketch. (a) g(0) = 1, g'(0) = 0, g(2) = 0, g'(2) = 1 is continuous everywhere. (b) y = g(x) is increasing but at a decreasing rate. (c) g is differentiable at x = 2 but g is not continuous at x = 2. (d) lim g(x) and lim g(x) exist x→2+ x→2¯ but lim g(x) does not exist. x→2
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