Given $|f(x) - f(y)| \leq M|x-y|^2$ , prove that f is constant.
Let f be differentiable on R and suppose that there exists M > 0 such that, for any x, y $\in$ R, $|f(x) - f(y)| \leq M|x-y|^2$. Prove that f is a constant function.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
2.1K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 976 views
- $8.00
Related Questions
- Compute the curl of $F=(x^2-\sin (xy), z-cox(y), e^{xy} )$
- Compute $\lim\limits_{x \rightarrow 0} \frac{1-\frac{1}{2}x^2-\cos(\frac{x}{1-x^2})}{x^4}$
- What is f(x). I've been trying to understand it for so long, but I always get different answers, I feel like I'm going crazy. Please someone explain it and read my whole question carefully.
- Find the average value of the function $\frac{\sin x}{1+\cos^2 x}$ on the interval $[0,1]$
- A question about the mathematical constant e.
- Find $\int x \sqrt{1-x}dx$
- Help with Norms
- Calculus Question