函数 ｙ =Ａ(ｘ)Ｂ(ｘ) (Ａ(ｘ)、Ｂ(ｘ)都是二次三项式 ,二次项系数不为零 )的极值问题 ,是中学数学颇受注意的内容之一 ,也是考试常见的题型。现拟借助函数 ｙ =ｘ± 1ｘ 的单调性来探讨这类函数的极值问题求解的通法。下面先来探讨一下 ｙ =ｘ± 1ｘ(ｘ≠ 0 )的单调性与极值 The function y = A(x)B(x) (A(x), B(x) are quadratic trinomials, and the quadratic coefficient is not zero) is the extreme value problem of high school mathematics. One of the common questions in the exam. It is proposed to use the monotony of the function y =x±1x to explore the general method for solving the extreme problem of such functions. Let’s first discuss the monotonicity and extremum of y =x± 1x(x≠ 0 )