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If f'(x) <= f(x) for all x, and f (0)=0, does f (x) = 0 for all x? [Advanced Calculus]
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smilius is
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Advanced Calculus
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f is defind as having a second derivative.
I assume f (x) = 0 (I can't find a counter example). I also a suspect I'm supposed to use the second derivative to prove that f'(x) = 0, but I don't see how to do that. What theorem do I need for this? How do I start the proof?
EDIT: I should have stated that f:R->R. Resolved almost immediatly.
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