Solution
= Solution
\b[No.] The <Darboux theorem> says that every <derivative> has the intermediate-value property. Choose $\epsilon<1/3$. In a deleted neighborhood of $a$, the assumed <limit> puts $\phi(x)$ within $\epsilon$ of $\phi(a)+1$. Darboux's theorem applied between $a$ and any such $x$ would require values near $\phi(a)+1/2$, which that neighborhood excludes. This contradiction shows that $\phi$ cannot be a <derivative>.