Question

已知f(x)=ax的平方+bx,满足1≤f(-2)≤2,3≤f(1)≤4,求f(2)的最大值与最小值.

Answer 1

f(x)=ax^2+bx

f(-2)=4a-2b∈[1,2]

f(1)=a+b∈[3,4]

从而f(2)=4a+2b=1/3*f(-2)+8/3*f(1)=4a+2b∈[25/3,34/3]