This question examines the synthesis of inverse proportional function: master the coordinate characteristics of each point on the image of inverse proportional function, and find a resolution function by undetermined coefficient method; Understand the essence of coordinates and graphics; The properties of quadratic function can be used to solve the maximum problem. Shandong problem is recognized as difficult.

First, according to the coordinate characteristics of points on the inverse proportional function image, it is easy to get the root number 3 with k=2; Secondly, let BH be perpendicular to H, and determine point B according to the coordinate characteristics of each point on the inverse proportional function image.

Solution: (1) Substitute point A into y=k/x to get the root number 3* 1=2.

(2) Let BH be perpendicular to H. See here /exercise/math/798672 for the detailed answer, as shown in figure 1, and the inverse proportional function y = k/x (x > 0) The image passes through point A(2 root numbers 3, 1), the ray AB intersects with the inverse proportional function image at another point B( 1, a), the ray AC intersects with the y axis at point C, the angle BAC=75 degrees, the AD is perpendicular to the y axis, and the vertical foot is d. 。

(1) Find the value of k;

(2) Find the value of tan angle DAC and the analytical formula of straight line AC;

(3) As shown in Figure 2, M is a moving point on the inverse proportional function image above the line segment AC. The straight line L passing through M is perpendicular to the X axis, intersects with AC at N points, and connects CM to find a triangle. Maximum value of CMN area.