Find two non-negative numbers whose sum is 14 for which the product of their squares is as large as possible.
A) 0 and 14
B) 5 and 9
C) 7 and 7
D) 1 and 13

Question

Quizplus · Accepted Answer

The product of the squares of two numbers that sum to 14 is maximized when the numbers are equal, i.e., 7 and 7, because of the symmetry of the problem and the principle that the product of two numbers with a fixed sum is maximized when the numbers are as close to each other as possible.

Find Two Non-Negative Numbers Whose Sum Is 14 for Which