题目

The year was 1932. Amelia Earhart was flying alone from North America to England in a small one-engine airplane. At midnight, several hours after she had left Newfoundland, she ran into bad weather. To make things worse, her altimetre failed. (The altimetre shows the height of the plane above the ground.) At night and in a storm, a pilot is in great difficulty without an altimetre. At times, her plane nearly plunged into the Atlantic Ocean. Just before daylight, there was further trouble. Amelia noticed flames coming from the engine. Would she be able to reach land? There was nothing to do exc已知函数f(x)=x4-4x3+ax2-1在区间［0，1］上单调递增，在区间［1，2］上单调递减.（1）求a的值；（2）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)的图象上；（3）是否存在实数b,使得函数g(x)=bx2-1的图象与函数f(x)的图象恰有3个交点，若存在，请求出实数b的取值范围；若不存在，试说明理由.