QUESTION 8 Find two positive numbers whose product is 64 and whose sum is a minimun Write your answers in the blanks below and show your work separately. The first number is The second number is
QUESTION 8 Find two positive numbers whose product is 64 and whose sum is a minimun Write your answers in the blanks below and show your work separately. The first number is The second number is
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Question 8**
Find two positive numbers whose product is 64 and whose sum is a minimum. Write your answers in the blanks below and show your work separately.
- The first number is: [___________]
- The second number is: [___________]
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**Question 9**
*(No content available in the image for Question 9.)*
---
To solve this problem, apply the concept of optimization in algebra. Use the fact that if two positive numbers have a constant product, their sum will be minimized when the two numbers are equal (or as close as possible given the constraint).
For more detailed methods, consider applying calculus by defining one number as \( x \) and the other as \( \frac{64}{x} \). Then minimize the function \( f(x) = x + \frac{64}{x} \) using derivative techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23f54c76-b762-419b-8fbe-ee40e7662c11%2F523cce44-f85d-4651-b69c-57936e5fc397%2Fejowotj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 8**
Find two positive numbers whose product is 64 and whose sum is a minimum. Write your answers in the blanks below and show your work separately.
- The first number is: [___________]
- The second number is: [___________]
---
**Question 9**
*(No content available in the image for Question 9.)*
---
To solve this problem, apply the concept of optimization in algebra. Use the fact that if two positive numbers have a constant product, their sum will be minimized when the two numbers are equal (or as close as possible given the constraint).
For more detailed methods, consider applying calculus by defining one number as \( x \) and the other as \( \frac{64}{x} \). Then minimize the function \( f(x) = x + \frac{64}{x} \) using derivative techniques.
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