已知函数f(x)=x的四次方-4x的三次方+ax的平方-1在区间[0,1]上单调递增,在区间[1,2]上单调递减.
问题描述：
已知函数f(x)=x的四次方-4x的三次方+ax的平方-1在区间[0,1]上单调递增,在区间[1,2]上单调递减.
(1) 若点A(X0 ,f（X0）)在函数f(x)的图象上,求证：点A关于直线X=1的对称点B也在函数f(x)的图像上；
(2)是否存在实数b使得函数g(x)=x^4+bx^2+1(其中b小于4）的图像与f(x)的图象恰有3个交点,若有,求出实数b的范围,若不存在请说明理由.
答
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