This kind of question tells you that both the domain and the value domain are [a, b]. Of course, you have to determine when f(x) takes A and when it takes B, which is related to the increase or decrease of f(x) in the interval [a, b]. Because of the uncertainty of increase or decrease, you can't know when x=a or x=b, f(x) is the maximum. To determine the increase or decrease, it is natural to determine the relationship between the symmetry axis and the interval. There are three situations, namely, the symmetry axis is on the right side of the interval, the symmetry axis is on the left side of the interval, and the symmetry axis is within the interval. Then you can use it instead of the solution. If not, what do you want to do?