验证y=4x³-5x²+x-2,x∈[0,1]在给定区间上满足拉格朗日中值定理,并求出结论中ξ值
问题描述：
验证y=4x³-5x²+x-2,x∈[0,1]在给定区间上满足拉格朗日中值定理,并求出结论中ξ值
答
f(x)=4x³-5x²+x-2 f'(x)=12x^2-10x+1 f(1)-f(0)=f'(ζ)(1-0) 12ξ^2-10ξ+1=0
ζ=(10+2根号13)/24 或 ζ=(10-2根号13)/24 而ζ∈[0,1] 两个ζ均满足