若f(x)有二阶导数,且f(0)=f(1)=0,lim(x→0)[f(x)/x]=0,则在(0,1)内至少存在一点ξ,使f"(ξ)=0
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若f(x)有二阶导数,且f(0)=f(1)=0,lim(x→0)[f(x)/x]=0,则在(0,1)内至少存在一点ξ,使f"(ξ)=0
若f(x)有二阶导数,且f(0)=f(1)=0,lim(x→0)[f(x)/x]=0,则在(0,1)内至少存在一点ξ,使f"(ξ)=0
若f(x)有二阶导数,且f(0)=f(1)=0,lim(x→0)[f(x)/x]=0,则在(0,1)内至少存在一点ξ,使f"(ξ)=0
f(x)有二阶导数,则f(x)一阶导数及f(x)连续可导
f(x)/x→0(x→0)则f(x)→0(x→0)
而f(x)连续,则(x→0)时,f(x)→0=f(0)=0
则f(x)/x→0(x→0)=[(f(x)-f(0))/(x-0)]→0(x→0)
即f'(0)=0
因为f(0)=f(1)=0,根据罗尔中值定理在(0,1)内至少存在一点ξ1,使f'(ξ1)=0
有因为f'(0)=f'(ξ1)=0 而f(x)一阶导数连续可导
又满足罗尔中值定理
所以在(0,ξ1)即(0,1)内至少存在一点ξ,使f''(ξ)=0
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