求函数最值常应用基本不等式或求导法,但由于等号成立的条件较强,有时不能运用基本不等式,或者导函数结构比原函数还复杂,须换元后再应用求导法.针对这个问题,已有定理1和定理2分别解决了“积一定,和最小”类型以及“和一定,积最大”类型的函数最值问题.本文提出定理1’,定理2’分别解决“积一定,和最大”类型以及“和一定,积最小”类型函数最值问题,并归纳出一般定理3解决此类型函数最值问题. However, the basic inequality or derivation method is most often used to find a function. However, since the condition of equal sign is strong, sometimes basic inequalities can not be used or the structure of the derivative function is more complex than the original one. This problem has been solved theorem 1 and theorem 2, respectively, the most value problem of the function “”, “and the smallest ” and the type of “and certain, product maximum Solve the most value problems of ”a certain product, and largest“ type and ”and a certain product of the smallest" type function, and sum up the general theorem 3 to solve the most value problem of this type of function.