Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum.
(a) Make a table of values, like the following one, so that the sum of the numbers in the first two columns is always 23. On the basis of the evidence in your table, estimate the answer to the problem.

(b) Use calculus to solve the problem and compare with your answer to part (a).

First number Second number Product 22 22 21 42 20 60