Find two positive numbers whose sum is 110 and whose product is a maximum.

(a) Analytically complete six rows of a table such as the one below. 

(b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the solution.

(c) Write the product P as a function of x.

(d) Use a graphing utility to graph the function in part (c) and estimate the solution from the graph.
(e) Use calculus to find the critical number of the function in part (c). Then find the two numbers.

First Number, x 10 20 Second Number 110 10 110 - 20 Product, P 10(110 - 10) 20(110 - 20) = 1000 = 1800