Let a,b $\displaystyle \in $ R, a < b and consider f : [a,b] $\displaystyle \longrightarrow$ R continuous on [a,b], differentiable on (a,b) and such that f(a) = f(b) = 0. Show that for any M > 0 there exists c $\displaystyle \in$ (a,b) such that:

M * f(c) + f '(c) = 0

Any help appreciated! Please and thank you