I'm trying to answer this problem: Consider a real function f, bandlimited by frequency $\omega_m$, which satisfy $integral(f(x)^2dx)=c$

Is the first derivative of this function limited in absolute value? That is, is there an expression $A(\omega_m,c)$ for which $f'(x)<A(\omega_m,c)$ for all x?  

Thank for the help!