函数与导数知识点.doc

:..数知识点【重点知识整合】\*MERGEFORMAT导数的定义:设函数\*MERGEFORMAT在\*MERGEFORMAT处附近有定义,当自变量在\*MERGEFORMAT处有增量\*MERGEFORMAT时,则函数\*MERGEFORMAT相应地有增量\*MERGEFORMAT,如果\*MERGEFORMAT时,\*MERGEFORMAT与\*MERGEFORMAT的比\*MERGEFORMAT(也叫函数的平均变化率)有极限即\*MERGEFORMAT无限趋近于某个常数,我们把这个极限值叫做函数\*MERGEFORMAT在\*MERGEFORMAT处的导数,记作\*MERGEFORMAT,即\*:在定义式中,设\*MERGEFORMAT,则\*MERGEFORMAT,当\*MERGEFORMAT趋近于SKIPIF1<0\*MERGEFORMAT时,\*MERGEFORMAT趋近于\*MERGEFORMAT,因此,导数的定义式可写成\*MERGEFORMAT.\*MERGEFORMAT导数的几何意义:导数\*MERGEFORMAT是函数\*MERGEFORMAT在点\*MERGEFORMAT的处瞬时变化率,它反映的函数\*MERGEFORMAT在点\*\*MERGEFORMAT上点(\*MERGEFORMAT),如果\*MERGEFORMAT在点\*MERGEFORMAT可导,则曲线\*MERGEFORMAT在点(\*MERGEFORMAT)处的切线方程为\*MERGEFORMAT注意:“过点SKIPIF1<0\*MERGEFORMAT的曲线的切线方程”与“在点SKIPIF1<0\*MERGEFORMAT处的切线方程”是不相同的,后者SKIPIF1<0\*MERGEFORMAT必为切点,<0\*MERGEFORMAT导数的物理意义:函数\*MERGEFORMAT在点SKIPIF1<0\*MERGEFORMAT处的导数\*MERGEFORMAT就是物体的运动方程\*MERGEFORMAT在点SKIPIF1<0\*MERGEFORMAT时刻的瞬时速度SKIPIF1<0\*MERGEFORMAT,即\*:\*MERGEFORMAT(SKIPIF1<0\*MERGEFORMAT为常数);\*MERGEFORMAT(\*MERGEFORMAT);\*MERGEFORMAT;\*MERGEFORMAT;\*MERGEFORMAT;\*MERGEFORMAT;\*MERGEFORMAT;\*:法则SKIPIF1<0\*MERGEFORMAT:\*MERGEFORMAT;法则SKIPIF1<0\*MERGEFORMAT:\*MERGEFORMAT,\*MERGEFORMAT;法则\*MERGEFORMAT:\*:设函数\*MERGEFORMAT在点\*MERGEFORMAT处有导数\*MERGEFORMAT,函数\