作业帮设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
来源：学生作业帮助网 编辑：作业帮 时间：2024/07/14 03:41:24
![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)
x){n_= t>":Q')Ɏ=߽V(dZ~Γ S@Z Hg3ԕif @vB ZnT?AQEUiٌd7
MԸ
-4 ,cFF&T)XauOh{6nBM 7udM[Ը4 CDE4Lmԧq$#<;P$ jG.W
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
设f(x)在[a,b]上连续,且a
设函数f(x)在[a,b]上连续,a
设f(x)在[a,b]上连续,且a
设f(x)在[a,b]上连续,且a
设f(x)在[a,b]上连续,a
设函数f(x)在[a,b]上连续,a
设函数f(x)在[a,b]上连续,在(a,b)内可导且f'(x)
设函数f(x)在[a,b]上连续,在(a,b)上可导且f'(x)
【50分高数微积分题】设f(x)在[a,b]上连续,在（a,b）内可导 f(a)f(b)>0 f(a)f[(a+b)/2]
证明:设f(x)在[a,b]上连续,在(a,b)内可导,(0
设f(x)在[a,b]上连续,在(a,b)上可导(0
设函数f(x)在[a,b]上连续,在(a,b)内可导(0
设f(x)在[a,b]上连续,在(a,b)内可导,(0
设f(x)在[a,b]上连续,在(a,b)内可导(0
设f(x)在[a,b]上连续,在(a,b)内可导(0
设函数f(x),g(x)在区间[a,b]上连续,且f(a)
设f（x）在[a,b]上连续,在（a,b）内二阶可导,且f(a)f(b)＜0,f'(c)=0.a
证明设f(x)在有限开区间(a,b)内连续,且f(a+) ,f(b-)存在,则f(x)在(a,b)上一致连续.