Let $a,b,c$ be real numbers defined such that:
$f(x) = \begin{cases} \displaystyle\frac{1}{|x|}, & \mbox{if } |x| >c \\ \\ a+bx^2, & \mbox{if } |x| \leq c \end{cases}$
Find $a,b$ in terms of $c$ such that $f$ is differentiable at $c$.
The issue I am having is what cases do I have to consider? I think $c<0$ and $c\geq 0$ . But then, what is the expression of $f(x)$ in each case ?
Thank you in advance