设f(x)在[a,b]上连续,在[a,b]内可导,且f(a)=f(b)=0.试证在(a,b)内至少存在一点ζ,f'（ζ）-2ζf（ζ）=0

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设f(x)在[a,b]上连续,在[a,b]内可导,且f(a)=f(b)=0.试证在(a,b)内至少存在一点ζ,f'（ζ）-2ζf（ζ）=0
设f(x)在[a,b]上连续,在[a,b]内可导,且f(a)=f(b)=0.试证在(a,b)内至少存在一点ζ,f'（ζ）-2ζf（ζ）=0

设f(x)在[a,b]上连续,在[a,b]内可导,且f(a)=f(b)=0.试证在(a,b)内至少存在一点ζ,f'（ζ）-2ζf（ζ）=0
F(x)=f(x)/x^2,
G(x)=f(x)e^(-x^2)
G(a)=G(b)=0
G'(x)=e^(x^2)(f'(x)-2xf(x))
罗尔定理G'(ζ)=0 即
f'（ζ）-2ζf（ζ）=0

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