Question

manisha has two positive numbers, and the product of them is 81. what is the minimum sum that she can obtain by these numbers? explain why there can not be a largest sum

Answer 1

S(x) = x + 81/x

S'(x) = 1 - 81/x² = 0

81/x² = 1

x² = 81

x = 9

S(x) = 9 + 81/9 = 9 + 9 = 18

The minimum sum is 18.

S''(9) = 1 + 162/9³ > 0, so there can not be a largest sum.