The geometric meaning of the required maximum is the difference between one point (x, 0) and two points (1, 2) and (3, 3) on the X axis.
The difference between the two sides of the display triangle is smaller than the third side.
Therefore, when (x, 0), (1, 2) and (3, 3) are three * * lines, the distance difference is the largest.
Because (1, 2) is close to the X axis.
That is, this value is the distance from the intersection of a straight line composed of two points (1, 2) and (3,3) and the X axis to (1, 2).
The straight line formed by (1, 2) and (3, 3) is x-2y+3=0, and the equation combined with the x axis is y=0.
The coordinate of (x, 0) is (-3, 0).
The distance from (-3,0) to (1, 2) is 2√5.
Therefore, the maximum value of fx is 2√5.