设f(x)在[0,2]上连续,在(0,2)上可微,且f(0)*f(2)>0,f(0)*f(1)
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![设f(x)在[0,2]上连续,在(0,2)上可微,且f(0)*f(2)>0,f(0)*f(1)](/uploads/image/z/8580247-7-7.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5B0%2C2%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%280%2C2%29%E4%B8%8A%E5%8F%AF%E5%BE%AE%2C%E4%B8%94f%280%29%2Af%282%29%3E0%2Cf%280%29%2Af%281%29)
设f(x)在[0,2]上连续,在(0,2)上可微,且f(0)*f(2)>0,f(0)*f(1)
设f(x)在[0,2]上连续,在(0,2)上可微,且f(0)*f(2)>0,f(0)*f(1)
设f(x)在[0,2]上连续,在(0,2)上可微,且f(0)*f(2)>0,f(0)*f(1)
令F(x)=f(x)*e^x,由已知有存在,x1属于(0,1),x2属于(1,2)使F(x1)=0,F(x2)=0,由罗尔中值定理有,存在ζ∈(x1,x2),使F‘(x)=0,化简得f'(ζ)=f(ζ).
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