All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
Monotonic Function Decomposition (Posted on 2020-04-08) Difficulty: 3 of 5
Many real-valued functions f:R->R have a decomposition f=up+down into two strictly monotonic components, one increasing, one decreasing. For example, if f(x)=x2, one can choose up(x)=|x|max(x,0)+x and down(x)=|x|max(-x,0)-x.

1. Find a monotonic decomposition of the cosine.

2. Find a differentiable function f:R->R without such decomposition.

3. Which slightly stronger condition than differentiability ensures that a monotonic decomposition exists? Provide a formula for suitable up's and down's.

No Solution Yet Submitted by JLo    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPart 1Steve Herman2020-04-09 20:01:10
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information