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在数学学习中,我们经常会遇到一类问题,那就是证明不等式恒成立或在不等式恒成立的条件下,求其中参数的取值范围。其问题的本质就是研究函数的变化情况,研究函数值的范围。导数作为研究函数单调性的有力武器,在这类问题中发挥了巨大的作用。导数反映了函数值的变化情况,我们可以利用导函数研究函数的单调性。对于函数y=f(x),在其定义域D内,若f′(x)>0,则y=f(x)在D上是增加的,反之,若y=f(x)在D上是增加的,则f′(x)≥0;若f′(x)<0,则y=f(x)在D上是减少的,反之,若y=f(x)在D上是减少的,则f′(x)≤0。明确了函数
In mathematics learning, we often encounter a class of problems, that is, to prove that the inequality is always established or in the inequality is established, the range of parameters. The essence of the problem is to study the changes of the function and study the range of the function value. Derivatives, as a powerful weapon for studying monotonicity of functions, play a huge role in such problems. Derivatives reflect the change of function values, and we can use the derivative function to study the monotonicity of the function. For the function y = f (x), y = f (x) is increased on D if f ’(x)> 0 in its domain D. Conversely, if y = f F ’(x) ≥0; if f’ (x) <0, then y = f (x) decreases on D, whereas if y = f Decrease, then f ’(x) ≤0. Clear function