f is continues in [0,1] and differentiable in (0,1)
f(0)=0 and for x\in(0,1) |f'(x)|<=|f(x)| and 0<a<1 prove:
(i)the set {|f(x)| : 0<=x<=a} has maximum
(ii)for every x\in(0,a] this innequality holds \frac{f(x)}{x}\leq max{|f(x)|:0<=x<=a}
(iii)f(x)=0 for x\in[0,a]
(iiiן)f(x)=0 for...