对勾函数最值的十种求法

关于求函数最小值的十种解法1、均值不等式EMBEDEquation.3，EMBEDEquation.3，当且仅当，即的时候不等式取到“=”。当的时候，二、法若的最小值存在，则必需存在，即或（舍）找到使时，存在相应的即可。通过观察当的时候，三、单调性定义设EMBEDEquation.3当对于任意的，只有EMBEDEquation.3时，EMBEDEquation.3，此时单调递增；当对于任意的，只有EMBEDEquation.3时，EMBEDEquation.3，此时单调递减。当取到最小值，四、复合函数的单调性在单调递增，在单调递减；在单调递增又EMBEDEquation.3EMBEDEquation.3EMBEDEquation.3EMBEDEquation.3EMBEDEquation.3原函数在上单调递减；在上单调递增即当取到最小值，五、求一阶导当时，，函数单调递减；当时，，函数单调递增。当取到最小值，六、三角代换令，，则当，即时，，，显然此时七、向量，EMBEDEquation.3EMBEDEquation.3根据图象，为起点在原点，终点在EMBEDEquation.3图象上的一个向量，的几何意义为在上的投影，显然当时，取得最小值。此时，，八、图象相减，即表示函数和两者之间的距离求，即为求两曲线竖直距离的最小值平移直线，显然当与相切时，两曲线竖直距离最小。关于直线轴对称，若与在处有一交点，根据对称性，在处也必有一个交点，即此时与相交。显然不是距离最小的情况。所以，切点一定为点。此时，，九、平面几何依据直角三角形射影定理，设，则显然，为菱形的一条边，只用当EMBEDEquation.3，即为直线和之间的距离时，取得最小值。即四边形为矩形。此时，，即，十、对应法则设EMBEDEquation.3EMBEDEquation.3，，对应法则也相同EMBEDEquation.3左边的最小值右边的最小值EMBEDEquation.3（舍）或当，即时取到最小值，且_1271079234.unknown_1271079341.unknown_1271079370.unknown_1271079371.unknown_1271079372.unknown_1271079373.unknown_1271079379.unknown_1271079401.unknown_1271079402.unknown_1271079403.unknown_1271079404.unknown_1271079405.unknown_1271079406.unknown_1271079407.unknown_1271079408.unknown_1271079409.unknown_1271079410.unknown_1271079431.unknown_1271079465.unknown_1271079466.unknown_1271079467.unknown_1271079510.unknown_1271079607.unknown_1271079659.unknown_1271079674.unknown_1271079718.unknown_1271079726.unknown_1271079788.unknown_1271079789.unknown_1271079928.unknown_1271079944.unknown_1271080005.unknown_1271080178.unknown_1271080265.unknown_1271080266.unknown_1271080297.unknown_1271080324.unknown_1271080473.unknown_1271080474.unknown_1271080538.unknown_1271080554.unknown_1271080559.unknown_1271080576.unknown_1271080597.unknown_1271165115.unknown_1271165116.unknown_1271165117.unknown_1271165118.unknown_1271165119.unknown_1271165120.unknown_1271165143.unknown_1271165144.unknown_1271165145.unknown_1271165221.unknown_1271165356.unknown_1271165389.unknown_1271165402.unknown_1271165414.unknown_1271165483.unknown_1271165484.unknown_1271165492.unknown_1271165737.unknown_1271165738.unknown_1271165752.unknown_1271165762.unknown_1271165791.unknown_1271165809.unknown_1271165971.unknown_1271165990.unknown_1271166004.unknown_1271166042.unknown_1271166057.unknown_1271166110.unknown_1271166179.unknown_1271166203.unknown_1271166256.unknown_1271166264.unknown_1271166358.unknown_1271166386.unknown_1271166427.unknown_1271166665.unknown_1271166729.unknown_1271166739.unknown_1271166790.unknown_1271166812.unknown_1271166919.unknown_1271166936.unknown_1271167019.unknown_1271167044.unknown_1271167089.unknown_1271167118.unknown_1271167143.unknown_1271167188.unknown_1271167940.unknown_1271167999.unknown_1271168001.unknown_1271168097.unknown_1271168108.unknown_1271168109.unknown_1271168129.unknown_1271168145.unknown_1271168180.unknown_1271168202.unknown_1271168216.unknown_1271168279.unknown_1271168303.unknown_1271190049.unknown_1271190757.unknown_1271190769.unknown_1271190770.unknown_1271190816.unknown_1271190825.unknown_1271190844.unknown_1271190855.unknown_1271190865.unknown_1271190907.unknown_1271190952.unknown_1271190965.unknown_1271190988.unknown_1271191016.unknown_1271191041.unknown_1271191056.unknown_1271191057.unknown_1271191058.unknown_1271191059.unknown_1271191060.unknown_1271191069.unknown_1271191070.unknown_1271191071.unknown_1271191072.unknown_1271191073.unknown_1271191496.unknown_1271191506.unknown_1271191641.unknown_1271191704.unknown_1271191747.unknown_1271191834.unknown_1271191908.unknown