Question

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

Answer 1

If \(f(x)=0\) for all \(x\geq0\), then \(f'(x)=0\) so the statement that \(|f'(x)|<|f(x)|\) is false.

Answer 2

Basically, this implies a contradiction. So I don't think this statement is true.

Answer 3

any question regarding to this?