Using differentiation to find maximum length problems

Click For Summary

Homework Help Overview

The problem involves finding the maximum value of the sum of the lengths of segments AB and AC, where AB lies on the diameter of a circle with a radius of 1, and angle BAC is a right angle. The context is rooted in geometry and optimization, specifically using differentiation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the problem and the choice of parameters, with one suggesting the x-coordinate of point A as a potential parameter. There are inquiries about the correctness of visual representations and calculations related to the problem.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to parameterization and expressing uncertainty about their setups. Some guidance has been offered regarding the coordinate system and lengths involved, but no consensus has been reached on the best method to proceed.

Contextual Notes

Participants are working within the constraints of the problem as stated, including the fixed radius of the circle and the right angle condition. There is an acknowledgment of confusion regarding the initial setup and parameters to use.

lmstaples
Messages
31
Reaction score
0

Homework Statement



The line segment AB lies on a diameter of a circle of radius 1, and the angle BAC is a right angle.

Find the greatest possible value of the sum of the lengths of AB and AC.


Homework Equations





The Attempt at a Solution



I have no idea what parameters to use or how to set up the problem.

Any help would be much appreciated.
 

Attachments

  • image.jpg
    image.jpg
    37.5 KB · Views: 508
Physics news on Phys.org
lmstaples said:

Homework Statement



The line segment AB lies on a diameter of a circle of radius 1, and the angle BAC is a right angle.

Find the greatest possible value of the sum of the lengths of AB and AC.


Homework Equations





The Attempt at a Solution



I have no idea what parameters to use or how to set up the problem.

Any help would be much appreciated.

Why not try picking the parameter to be the x coordinate of A?
 
check out the attachment, does that seem right?
 

Attachments

  • image (1).jpg
    image (1).jpg
    26 KB · Views: 555
lmstaples said:
check out the attachment, does that seem right?

Well, you ignored my advice on which parameter to use, so apparently you weren't all that confused to begin with. Yes, it looks ok.
 
Haha sorry, I had so many ideas of ways to do it and that's the only one I managed to fully work through :)
 
Here (I think) is what Dick was suggesting: set up a coordinate system so the origin is at the center of the circle, A is at (-1, 0), and the y-axis is parallel to BC. Then AB has length x+ 1 and BC has length \sqrt{1- x^2}.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
Replies
10
Views
3K
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 30 ·
2
Replies
30
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K