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

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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
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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
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

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

∵f(a)=f(b)=0 f(c)>0,且a∴f(x)为凸函数,即f '' (x) <0
∵f'(x)在[a,b]上连续
∴至少存在一点m属于(a,b)使得f '' (m) <0