$\displaystyle \text{Suppose } a, c \in \mathbb{R}, c > 0, f \in C[-1, 1],$

$\displaystyle f(x) = \begin{cases} x^a sin(|x|^{-c}) & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}$

$\displaystyle \text{Show } f \in C^{1}[-1, 1] \iff a > 1 + c.$

What do I do here? I just did a proof that showed that f is bounded iff a => 1 + c (and I had a tough time with that). Can I use that result to show continuity whenever a > 1 + c, or is there more to it? And what to do about the "iff"?

Please, please, please be clear and explicit in your replies--I am still a rookie at this stuff.