1. 导数决定了可导函数的重要性质，包括单调性与极值，是已经函数性质的有力工具。本节介绍一阶导数和函数单调性之间的关系。<br />根据直观认识，由于导数是函数变化率的极限，因此如果在![](https://cdn.nlark.com/yuque/__latex/9dd4e461268c8034f5c8564e155c67a6.svg#card=math&code=x&id=hNIIM)点处它的值为正，则在该点处自变量增大时函数值也增大；如果为负，则自变量增大时函数值减小。假设在区间![](https://cdn.nlark.com/yuque/__latex/2c3d331bc98b44e71cb2aae9edadca7e.svg#card=math&code=%5Ba%2Cb%5D&id=kH2A6)内连续，在区间![](https://cdn.nlark.com/yuque/__latex/2d05e1f15387f87456155cd96cc06235.svg#card=math&code=%28a%2Cb%29&id=nibHc)内可导。如果在区间![](https://cdn.nlark.com/yuque/__latex/2d05e1f15387f87456155cd96cc06235.svg#card=math&code=%28a%2Cb%29&id=N2rxU)![](https://cdn.nlark.com/yuque/__latex/634e0231a21a388254e137f1d5518da8.svg#card=math&code=f%27%28x%29%3E0&id=hPpB7),单调递增，如果在区间![](https://cdn.nlark.com/yuque/__latex/2d05e1f15387f87456155cd96cc06235.svg#card=math&code=%28a%2Cb%29&id=Fea5C)![](https://cdn.nlark.com/yuque/__latex/0f840bc0209c8857ac5d2a2a1a3bd596.svg#card=math&code=f%27%28x%29%3C0&id=gNaHe),单调递减