高中数学新课程打破先讲极限后讲导数的顺序 ,直接通过实际背景和具体应用实例 ,即通过与社会生活联系紧密的速度、膨胀率、增长率等变化率引入导数 ,旨在用导数反映的变化率研究初等函数的性质 .本文通过利用导数对初等数学中较为复杂的解 (证明 )不等式、求函数最值、证明函 The new high school mathematics curriculum breaks the precondition of explaining the order of the derivatives and introduces the derivative directly through the actual background and specific application examples, that is, through the rate of change of the speed, expansion rate and growth rate closely related to social life, The rate of change study the nature of the elementary function.This paper through the use of derivatives of elementary mathematics more complex solutions (proof) inequality, find the value of the function,