Optimizing the Sum of a Number and its Reciprocal in Calculus

  • Context: Undergrad 
  • Thread starter Thread starter aMo0oDi
  • Start date Start date
  • Tags Tags
    Calculus
Click For Summary

Discussion Overview

The discussion revolves around a calculus problem involving the optimization of the sum of a positive number and its reciprocal. Participants seek to minimize the function defined by this sum.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents the function to minimize as f(x) = x + 1/x.
  • Another participant expresses confusion about how the function x + 1/x was derived.
  • A clarification is provided that x represents a number and 1/x represents its reciprocal, leading to the expression x + 1/x.
  • Participants discuss the need for understanding derivatives in the context of optimization.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing varying levels of understanding and confusion regarding the problem and its solution.

Contextual Notes

Some participants have not fully grasped the derivation of the function or the concept of optimization, indicating potential gaps in foundational knowledge.

aMo0oDi
Messages
10
Reaction score
0
new calculus problem.. HELP!

Hi there... i need a help with this question as soon as possible...

Find a positive number such that the sum of the number and its reciprocal is as small as possible..?
 
Physics news on Phys.org
Minimize f(x) = x + 1/x.
 
i'm kind of lost here, i need a full answer
 
Well, I'm not going to give it to you... How lost are you exactly? Do you know how to calculate the derivative of x + 1/x?
 
actually, i don't know how you get x + 1/x.. i can calculate its derivative though.. please explain the way the you got x + 1/x..

thanks..
 
x = a number.
1/x = that number's reciprocal.

x + 1/x = a number plus its reciprocal.
 
thanks a lot.. i appreciate your help :)
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 24 ·
Replies
24
Views
7K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 18 ·
Replies
18
Views
4K