Differentiable Proof

Let a,b $\in$ R, a < b and consider f : [a,b] $\longrightarrow$ 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 $\in$ (a,b) such that:

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

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