把正数a分成若干部分,然后将各部分乘起来,要使得乘积最大,应当怎样分法?这个问题虽然简单,做起来却很有意思.我们由均值不等式知道,在各数之和为定值时,要使它们的乘积取最大值,就必须各数相等.所以数a必须分成相等的若干部分.然而,究竟平分成几部分呢?用微积分的方法可以证明,只有当把已知数a平分成的各部分和e最接近时,乘积才取得最大值. Divide the positive number a into several parts, and then multiply each part, to maximize the product, how to divide? This question is simple, but it is very interesting to do. We know from the mean inequality that the sum of the numbers is fixed In order to make their products take maximum values, the numbers must be equal. Therefore, the number a must be divided into equal parts. However, exactly divided into several parts? Using the method of calculus can prove that only when the known number The product is maximized when the parts a and b are nearest to each other.