The difficulty of the three small questions in this question is gradually increasing. It is the finale to examine students' ability to grasp the monotonicity of functions in depth, which requires higher thinking. See the answer /exercise/math/804062/ From the process of solving problems, it is very important to guide the reasonable deformation of the resolution function, because it directly affects the judgment of derivative symbols and is an important breakthrough in solving problems?

The function f (x) = e x-e (-x)-2x is known.

(1) Discuss the monotonicity of f(x);

(2) let g(x)=f(2x)-4bf(x), when x >; 0, g(x)>0, and find the maximum value of b;

(3) Known 1.4 142