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nhrock3
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2.b)
f is continues in [0,1] and differentiable in (0,1)
f(0)=0 and for [tex]x\in(0,1)[/tex] |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 [TEX]\frac{f(x)}{x}\leq max{|f(x)|:0<=x<=a}[/TEX]
(iii)f(x)=0 for [TEX]x\in[0,a][/TEX]
(iii)f(x)=0 for [TEX]x\in[0,1][/TEX]
in each of the following subquestion we can use the previosly proves subquestion.
f is continues in [0,1] and differentiable in (0,1)
f(0)=0 and for [tex]x\in(0,1)[/tex] |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 [TEX]\frac{f(x)}{x}\leq max{|f(x)|:0<=x<=a}[/TEX]
(iii)f(x)=0 for [TEX]x\in[0,a][/TEX]
(iii)f(x)=0 for [TEX]x\in[0,1][/TEX]
in each of the following subquestion we can use the previosly proves subquestion.