Show that the function f : R → R given by f(x) = x/(1+|x|) is increasing.
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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Question
Show that the function f : R → R given by f(x) = x/(1+|x|) is increasing.
Expert Solution
Step 1
To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.
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