Let f be any function on the real line and suppose that: |f(x)-f(y)|<=|x-y|^2 for all x,y in R. Prove that f is a constant function. Note: "<=" reads "less than or equal to"
The Attempt at a Solution
I have tried proof by contradiction, it seems to be the most obvious route in proving this statement. I started by assuming that there exists x,y in the domain of the function f(x) such that f(x) is not equal to f(y). I wasn't really able to proceed much further from there. Any help towards finishing this proof or perhaps a different approach would be greatly appreciated.