我们知道,如果函数 f(x)、g(x)在点 x_0连续,则函数 max(f(x),g(x))在点 x_0亦连续。现在要问:如果函数 f(x)、g(x)在 x_0点可导,函数 max(f(x),g(x))是否在点 x_0亦可导呢?下面的定理1和定理2给出了判别函数 max(f(x),g(x))可导的充分条件。定理1 如果函数 f(x)、g(x)在 x_0点可导,且f(x_0) We know that if the functions f(x) and g(x) are continuous at the point x_0, then the function max(f(x), g(x)) is also continuous at the point x_0. Now to ask: If the functions f(x) and g(x) can be conducted at the x_0 point, can the function max(f(x), g(x)) lead at the point x_0? The following theorems 1 and theorems 2 The sufficient condition of the discriminant function max(f(x), g(x)) is given. Theorem 1 If functions f(x), g(x) are lead at x_0, and f(x_0)