Question: 8. (10%) Suppose f : [0,1] > R is continuous, f is differentiable on (0,1), and f(0) = 0. Assume that |f'(:c)| 5 |f(:.-:)| for

8. (10%) Suppose f : [0,1] > R is continuous, f is differentiable on (0,1), and f(0) = 0. Assume that |f'(:c)| 5 |f(:.-:)| for all a: 6 (0,1). Prove that fizz) =0 for all :1: E [0.1]

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