# Math Help - Urgent Help!

1. ## Urgent Help!

Any answers to this would be greatly appreciated, bit of assessed work i'm really struggling on.

2. Originally Posted by pkr
The idea for the first parts is that if $\epsilon > 0$ and $x$ is a fixed point then we can take $\delta > 0$ small enough such that $|x-y|^{\alpha} < \epsilon$ for all $|x-y| < \delta$. Therefore, $|f(x)-f(y)| \leq |x-y|^{\alpha} < \epsilon$. Thus, $f$ is continous.

In the second part if $\alpha > 1$ then $|f(x)-f(y)| \leq |x-y|^{\alpha}$ then $| [f(x)-f(y)]/[x-y] | \leq |x-y|^{\alpha - 1}$. Notice the LHS has form of a derivative. Thus, what can you conclude?