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在高中数学中,有一类函数问题需要利用导数方法探究函数f(x)在区间D上是否穿过x轴单调递增或单调递减.对此类问题,许多学生找不到突破口,甚至束手无策.以下结合实例探讨判断函数f(x)在区间D上是否穿过x轴单调递增或单调递减的策略.1判断函数f(x)的值的符号例1已知a∈R,关于x的方程x/(x2+x+2)=a最多有()个实数解.A.1 B.2 C.3 D.4
In high school mathematics, there is a class of functional problems that require a derivative approach to explore whether monotonically increasing or monotonically decreasing function f (x) crosses the x-axis over interval D. Many students find no breakthrough or even helplessness with this type of problem. The strategy of judging whether the function f (x) monotonically increases or monotonously decreases through the x axis is discussed in conjunction with the example.Example 1 of the judgment value of the function f (x) is known a∈R, and the equation x / (x2 + x + 2) = a Up to () real solutions .A.1 B.2 C.3 D.4