Solution
= Solution
{c}
A <function> $f:(a,b)\to\mathbb R$ is \b[<differentiable> on $(a,b)$] if, for every $x\in(a,b)$, the finite <limit of a function>
$$
\boxed{f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h}
$$
exists. Here $h\ne0$ and is sufficiently small that $x+h\in(a,b)$. This <limit of a function> is the <derivative> of $f$ at $x$.