Question

设f(x）在【a,b】上连续,在(a,b)内二阶可导,且f(a)=f(b)=f(c),a

Answer 1

∵f(x）在[a,b]上连续,在(a,b)内二阶可导,且f(a)=f(b)=f(c)∴由罗尔中值定理得存在e1∈(a,c),使得f'(e1)=0;存在e2∈(c,b),使得f'(e2)=0;∴f'(e1)=f'(e2)=0由于f'(x)在[e1,e2]连续,(e1,e2)可导故存在e∈(e1,e2)使得f'...