Question

第三小题 要过程

Answer 1

依题意知：
-3<=f(1)<=3
-3<=f(4)<=3
即-3<=a+2<=3且
-3<=16a+5<=3
即-5<=a<=1且
-1/2<=a<=-1/8
可得：-1/2<=a<=-1/8(1)
因为a不等于0，所以f(x)是一二次抛物线，
抛物线f(x)=ax^2+x+1的对称轴为-1/(2a)
1<=-1/(2a)<=4,
即，x=-1/(2a),函数有极值，
则-3<=f[-1/(2a)]=1-1/(4a)<=3
即:-2<=1/(4a)<=4
即:-8<=1/(a)<=16
即:-8<=1/(a)<0或0<1/(a)<=16
a<=-1/8或1/16<=a<0(2)
综上可得:
-1/2<=a<=-1/8