Can anyone help on this problem:
Supposef is defined on (−∞,∞) and |f(x) − f(y)| ≤ K|x− y|^α
for all x, y E(−∞,∞) and some constants K and α> 0 .
Show that f is continuous on (−∞,∞) .
If α> 1 , show that f '(x) = 0 for all x E(−∞,∞)
Thank you.
Can anyone help on this problem:
Supposef is defined on (−∞,∞) and |f(x) − f(y)| ≤ K|x− y|^α
for all x, y E(−∞,∞) and some constants K and α> 0 .
Show that f is continuous on (−∞,∞) .
If α> 1 , show that f '(x) = 0 for all x E(−∞,∞)
Thank you.