(Ⅰ)设f(x),g(x)在(a,b)可微,g(x)≠0,且,求证:存在常数C,使得f(x)=Cg(x)(∈(a,b)); (Ⅱ)设f(x)在(—∞,+∞)二阶可导,且f(x)≤0,f"(x)≥0(x∈(—∞,+∞)).求证:f(x)为常数(x∈(—∞,+

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问题 (Ⅰ)设f(x),g(x)在(a,b)可微,g(x)≠0,且,求证:存在常数C,使得f(x)=Cg(x)(∈(a,b));
(Ⅱ)设f(x)在(—∞,+∞)二阶可导,且f(x)≤0,f"(x)≥0(x∈(—∞,+∞)).求证:f(x)为常数(x∈(—∞,+∞)).

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答案(Ⅰ)即证f(x)/g(x)在(a,b)为常数.由 [*]

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