Answer

Slope overload condition: $|dm/dt|_{max}\le\Delta f_s$. For $m=A_m\cos\omega_m t$, $|dm/dt|_{max}=A_m\omega_m$. So $f_m\le\Delta f_s/(2\pi A_m)$. Given $\Delta=0.1$V $f_s=10$kHz $A_m=1$V → $f_{max}=159$Hz. General $f_{max}=\Delta f_s/(2\pi A_m)$.