证明:g(x)=x²+ax+b,则 g( (x1+x2)/2)小于等于g(x1)+g(x2)的二分之一

问题描述:

证明:g(x)=x²+ax+b,则 g( (x1+x2)/2)小于等于g(x1)+g(x2)的二分之一

因为,g( (x1+x2)/2 )= (1/4)(x1+x2)² + (a/2)(x1+x2) + b ;(1/2)[g(x1)+g(x2)] = (1/2)(x1²+x2²) + (a/2)(x1+x2) + b ;可得:(1/2)[g(x1)+g(x2)] - g( (x1+x2)/2 )= (1/2)(x1²+x2²) ...