1 |
a |
∵
1 |
3 |
1 |
a |
∴f(x)在[1,3]上,N(a)=f(
1 |
a |
1 |
a |
∵f(x)=ax2-2x+1在区间[1,3]上的最大值为M(a),最小值为N(a),
∴①当1≤
1 |
a |
1 |
2 |
M(a)=f(3)=9a-5,N(a)=f(
1 |
a |
1 |
a |
g(a)=M(a)-N(a)=9a+
1 |
a |
②当2≤
1 |
a |
1 |
3 |
1 |
2 |
M(a)=f(1)=a-1,N(a)=f(
1 |
a |
1 |
a |
g(a)=M(a)-N(a)=a+
1 |
a |
∴g(a)=
|
1 |
3 |
1 |
a |
1 |
3 |
1 |
a |
1 |
a |
1 |
a |
1 |
a |
1 |
2 |
1 |
a |
1 |
a |
1 |
a |
1 |
a |
1 |
3 |
1 |
2 |
1 |
a |
1 |
a |
1 |
a |
|