Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I want to drift a $C^1$ function $g(x):\mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ to reach $"0"$ smoothly on some interval $[x_{1},x_{2}]$ and then drift it again to continue it's values on $(x_{2},\infty)$. I've found something about partitions of unity and bump functions but i'm a bit confused. Can i multiply $g(x)$ by the bump function that is $0$ on $[x_{1},x_{2}]$ and 1 outside it with just a small frame $(x_{1}-\epsilon,x_{1})$ in which it can fall from 1 to zero?

share|cite|improve this question

Yes, you can do exactly that. It is the nice thing about bump functions.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.