Let f:[0,infinity) - R be a differentiable function such that f'(x) = f(x) 0 for all x in [0,infinity). Construct a proof to show that f'(x) = f(x) for all x in [0,infinity).

Question

Let f:[0,infinity) -> R be a differentiable function such that f'(x) >= f(x) > 0 for all x in [0,infinity). Construct a proof to show that f'(x) >= f(x) for all x in [0,infinity).

Steve · Answer

You say f'(x) >= f(x) > 0 for all x in [0,∞) show that f'(x) >= f(x) for all x in [0,∞) Is that not the hypothesis already?