Numerical Graphical and Analytic Analysis 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. (The first two rows arc shown.) Use the table to guess the maximum product.
|First Number, x||Second Number||Product, P|
|10||110 - 10|
(b) Write the product P as a function of x.
(c) Use calculus to find the critical number of the function in part (b). Then find the two numbers.
(d) Use a graphing utility to graph the function in part (b) and verify the solution from the graph.
To calculate: The estimated maximum product for two numbers with sum 110 by completing the table given below.
Consider a number 30. As the sum of the two numbers needs to be 110, the second number would be,
Then the product would be,
Do the same for number 40, 50 and 60, 70, 80, 90
To calculate: The product as a function of x where, the sum of the two numbers is 110.
To calculate: The critical points of the function and the numbers such thattheir product is maximum.
To graph: The function obtained in part (b) which is and to verify the maxima obtained.
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