Problem 6: For each part below, find an equation f(x) with the stated properties, or if there are no examples, explain why not. You need not assume that f is a smooth function for this problem, but you should remark on on the continuity and differentiability of f. (a) Every real number is a fixed point. (b) There are no fixed points. (c) There are precisely 100 fixed points. (d) Every integer is a fixed point, and there are no others. (e) Every number except 0 is a fixed point. =
Problem 6: For each part below, find an equation f(x) with the stated properties, or if there are no examples, explain why not. You need not assume that f is a smooth function for this problem, but you should remark on on the continuity and differentiability of f. (a) Every real number is a fixed point. (b) There are no fixed points. (c) There are precisely 100 fixed points. (d) Every integer is a fixed point, and there are no others. (e) Every number except 0 is a fixed point. =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 6: For each part below, find an equation ☀
f(x) with the
stated properties, or if there are no examples, explain why not. You
need not assume that f is a smooth function for this problem, but you
should remark on on the continuity and differentiability of f.
(a) Every real number is a fixed point.
(b) There are no fixed points.
(c) There are precisely 100 fixed points.
(d) Every integer is a fixed point, and there are no others.
(e) Every number except 0 is a fixed point.
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