[分析]f is differentiable on R,f'(x)>f(x) and f(0)=0

[linshihhua (linshihhua)]

let f be a real-valued differentiable function on R such that f'(x)>f(x)

for all x in R. Assume that f(0)=0, show that f(x)>0 for all x>0

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推 peicachu    :f'(0)>f(0)=0, 局部遞增, f(c)>0 for c>0
推 zombiea     :g(x)= exp(-x)f(x), g(0)=0, g'(x)>0 for all x >0
→ zombiea     :hence, g(x)>0 for all x >0