In seventh grade mathematics, we usually encounter the problem of finding the maximum and minimum. Here are some common solutions:

Finding the maximum value by using axial symmetry

In some extreme problems, it can be solved by axisymmetric method. For example, at two points A and B on a straight line, we should find the point C on the same side of the straight line to minimize the sum of the distances between AC and BC. At this point, we can find the symmetrical point B' of point B about the straight line. If the line AB' intersects the straight line at point C, the sum of the distances between AC and BC is the smallest, and the minimum value is |AB'|.

The sum of two sides of a triangle is greater than the third side.

In some maximum problems, the minimum value of the sum of distances between multiple points is needed. At this time, you can connect some points in pairs, and choose any intersection point on these two connecting lines to minimize the sum of distances. For example, there are four points a, b, c and d on the plane. We need to find a point e between a, b, c and d to minimize AE+BE+CE+DE.

At this time, you can connect AC and BD, and choose an intersection e on these two lines, then AE+BE+CE+DE is the minimum value, and the minimum value is |AC|+|BD|.

Use the shortest line segment between two points.

In some maximum problems, the minimum distance between two points is required. At this time, we can connect these two points and choose a point on this straight line to minimize the distance difference between one point and two points on this line segment.

For example, there are two points a and b on the plane. If you want to find a point C between A and B, so that the lengths of AC and BC are equal, you can arbitrarily choose a point C on the vertical line of AB, then the lengths of AC and BC are equal, and the length is a fixed value AB/2.

The above are the common solutions to the maximum and minimum values in seventh grade mathematics. It should be noted that in solving practical problems, we need to analyze specific problems and choose appropriate solutions to solve them.