1. The problem statement, all variables and given/known data Let [a, b] be an interval in R, and f:[a, b] -> R be differentiable on [a, b]. Assume f(a) = 0, and that there is a number M such that [tex]\left|f'(x)\right| \leq M \left|f(x)\right|[/tex] for all x in [a, b]. Prove that f is identically 0 on [a, b]. 2. Relevant equations Mean Value Theorem? 3. The attempt at a solution I've tried this problem multiple times and I keep hitting a wall. I've tried to approach it through contradiction, letting c be some point in [a, b] such that f(c) > 0, but it always seems that we could find an M sufficiently large such that this is true.