Two numbers sum to 42. Find the two numbers whose product is maximum.
A) 21, 40
B) 7, 35
C) 6, 39
D) 21, 21
E) 14, 28

Question

Quizplus · Accepted Answer

Let the two numbers be x and 42-x. 
Their product is P(x) = x(42-x) = -x^2 + 42x
This is a quadratic function with a=-1, b=42, and c=0. 
The maximum value of the product occurs at x = -b/2a = -42/(-2) = 21.
Therefore, the two numbers are 21 and 21. 
Their product is 21*21 = 441, which is the maximum possible product. 
Thus, the answer is choice D.

Two Numbers Sum to 42