Question 1. For each set of conditions below, give an example of a function f that satisfies the given conditions; you should give the graph and formula for each function explicitly, and show that your function satisfies all the conditions in each part. (You may use piecewise-defined functions if needed.) (a) A function f that is strictly increasing on (-∞0, 0), strictly decreasing on (0, ∞o), and is concave up everywhere (except possibly at x = 0). (b) A function g that is twice differentiable, has exactly two inflection points, and exactly one local maximum point.
Question 1. For each set of conditions below, give an example of a function f that satisfies the given conditions; you should give the graph and formula for each function explicitly, and show that your function satisfies all the conditions in each part. (You may use piecewise-defined functions if needed.) (a) A function f that is strictly increasing on (-∞0, 0), strictly decreasing on (0, ∞o), and is concave up everywhere (except possibly at x = 0). (b) A function g that is twice differentiable, has exactly two inflection points, and exactly one local maximum point.
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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Please solve part a and part B of question
Transcribed Image Text:Question 1. For each set of conditions below, give an example of a function f that satisfies the given conditions;
you should give the graph and formula for each function explicitly, and show that your function satisfies all the
conditions in each part. (You may use piecewise-defined functions if needed.)
(a) A function f that is strictly increasing on (-∞0, 0), strictly decreasing on (0, 0), and is concave up everywhere
(except possibly at x = 0).
(b) A function g that is twice differentiable, has exactly two inflection points, and exactly one local maximum point.
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