1. ## [SOLVED] Urgent

Can anyone help on this problem:
Suppose
f is defined on (−∞,) and |f(x) f(y)| ≤ K|xy|^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.

2. If $\varepsilon > 0$ define $\delta = \left( {\frac{\varepsilon }{K}} \right)^\frac {1}{a}$.

3. is that only to show is continuous?

4. $\left| {f(x) - f(y)} \right| \le K\left| {x - y} \right|^a \Rightarrow \quad \left| {\frac{{f(x) - f(y)}}{{x - y}} - 0} \right| \le K\left| {x - y} \right|^{a - 1}$