Let the functionx) have the2 2nd derivative on the interval[o.andf(1)>0.lim(x)0.+x Proof: (1)The equation f(x) =0 has at least one real root in the interval (0,1):(2)The equation(x)f"(x)+[f"(x)2-0 has at least two different real roots in the interval (0,1).
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