设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)...设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)使f'(ξ)+f(ξ)/ξ=0,
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![设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)...设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)使f'(ξ)+f(ξ)/ξ=0,](/uploads/image/z/1826234-26-4.jpg?t=%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%5B0%2Ca%5D%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%880%2Ca%EF%BC%89%E5%8F%AF%E5%AF%BC%2C%E8%AF%81%E6%98%8E%E5%AD%98%E5%9C%A8%CE%BE%E2%88%88%EF%BC%880%2Ca%EF%BC%89...%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%5B0%2Ca%5D%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%880%2Ca%EF%BC%89%E5%8F%AF%E5%AF%BC%2C%E8%AF%81%E6%98%8E%E5%AD%98%E5%9C%A8%CE%BE%E2%88%88%EF%BC%880%2Ca%EF%BC%89%E4%BD%BFf%27%EF%BC%88%CE%BE%EF%BC%89%EF%BC%8Bf%EF%BC%88%CE%BE%EF%BC%89%2F%CE%BE%3D0%2C)
设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)...设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)使f'(ξ)+f(ξ)/ξ=0,
设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)...
设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)使f'(ξ)+f(ξ)/ξ=0,
设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)...设f(x)在[0,a]连续,在(0,a)可导,证明存在ξ∈(0,a)使f'(ξ)+f(ξ)/ξ=0,
如果f(x)=x,这道题不就证不了了吗?呃……我加一个条件吧,f(a)=0,这样好一点.设一个辅助函数F(x)=xf(x),显然有F(x)在[0,a]连续,在(0,a)可导,又因为F(0)=F(a)=0,根据罗尔中值定理,存在ξ∈(0,a)使F'(ξ)=ξf'(ξ)+f(ξ)=0 成立,又因为ξ不会为0,上式两端除以ξ即可得证.