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Let f be continuous on [ 0 , ∞ ) and differentiable on ( 0 ,...

Let f be continuous on [ 0 , ∞ ) and differentiable on ( 0 , ∞ ) . If f ( 0 ) = 0 and | f ′ ( x ) | ≤ | f ( x ) | for all x > 0 , then f ( x ) = 0 for all x ≥ 0 .

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Let f be continuous on [0,) and differentiable on (0,).

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