设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f‘(c)+f(c)=0设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f ‘(c)+f(c)=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证明 存在c∈(a,b)使f‘(c)+f(c)=0设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f ‘(c)+f(c)=0](/uploads/image/z/5349438-54-8.jpg?t=%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%88a%2Cb%EF%BC%89%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%EF%BC%88a%EF%BC%89%3Df%EF%BC%88b%EF%BC%89%3D0%E8%AF%81%E6%98%8E+%E5%AD%98%E5%9C%A8c%E2%88%88%EF%BC%88a%2Cb%EF%BC%89%E4%BD%BFf%E2%80%98%EF%BC%88c%EF%BC%89%2Bf%EF%BC%88c%EF%BC%89%3D0%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%88a%2Cb%EF%BC%89%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%EF%BC%88a%EF%BC%89%3Df%EF%BC%88b%EF%BC%89%3D0%E8%AF%81%E6%98%8E+%E5%AD%98%E5%9C%A8c%E2%88%88%EF%BC%88a%2Cb%EF%BC%89%E4%BD%BFf+%E2%80%98%EF%BC%88c%EF%BC%89%2Bf%EF%BC%88c%EF%BC%89%3D0)
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f‘(c)+f(c)=0设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f ‘(c)+f(c)=0
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f‘(c)+f(c)=0
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f ‘(c)+f(c)=0
若要证f ‘(c)+[f(c)]^2=0
设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f‘(c)+f(c)=0设f(x)在[a,b]上连续,在(a,b)内可导,且f(a)=f(b)=0证明 存在c∈(a,b)使f ‘(c)+f(c)=0
令F(x)=e^x * f(x)
则F(a)=F(b)=0
由中值定理有
存在c∈(a,b),F'(c)= e^cf(c)+e^cf'(c)= e^c(f'(c)+f(c))=0
即f‘(c)+f(c)=0
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