Let f: (0,1) --> R be any function with the following properties.
I know that f(x) = sin(x^2) follows the above properties. Thus, . But I can't prove this for any general function.
Any hintss to get me started?
An alternative that doesn't require the derivative of f(x) starts setting . Now setting we have and the condition 2) becomes...
... and the only value of that satisfies (1) is ...