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.

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- July 21st 2008, 12:14 PMGreen03[SOLVED] Urgent
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.

- July 21st 2008, 12:35 PMPlato
If define .

- July 21st 2008, 01:27 PMGreen03
is that only to show is continuous?

- July 21st 2008, 01:46 PMPlato