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Numerical, Graphical, and Analytic Analysis Find two positive numbers whose sum is 110
Chapter 3, Problem 1(choose chapter or problem)
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 are shown.) (b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.) (c) Write the product as a function of (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. xy
Questions & Answers
QUESTION:
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 are shown.) (b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.) (c) Write the product as a function of (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. xy
ANSWER:
Step 1 of 5
A)
First Number x |
Second number |
Product P1 |
10 |
110 - 10 = 100 |
10 ( 110 – 10 ) = 1000 |
20 |
110 – 20 = 90 |
20 ( 110 – 20 ) = 1800 |
30 |
110 – 30 = 80 |
30 ( 110 – 30 ) = 2400 |
40 |
110 – 40 = 70 |
40 ( 110 – 40 ) = 2800 |
50 |
110 – 50 = 60 |
50 ( 110 – 50 ) = 3000 |
60 |
110 – 60 = 50 |
60 ( 110 – 60 ) = 3000 |