Optimization of a rectangle's area in two parabolas

  • Thread starter cinematic
  • Start date
  • #1
cinematic
8
0

Homework Statement


Determine the maximum area of a rectangle formed in the region formed by the two curves
y1=x2 - k
y2=x2 + k


Homework Equations


The equations are given, I tried using k=1. so y1= x2 - 1, etc.


The Attempt at a Solution


Is it true that the rectangle has to be sideways (i.e. NOT parallel to the axes in order to maximize the area of the rectangle?)
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
774
Why take k = 1? Just leave it as k. Is this problem from a typical first year calculus text? The reason I ask is I would be very surprised if it is asking you to consider rectangles not parallel to the axes. I don't know offhand if the maximum would be attained by a slanted rectangle since I have never seen that problem worked, worked it myself, or even asked for that matter.
 
  • #3
cinematic
8
0
Actually, this is an extension on first-time calculus. Our teacher was suggesting if it was possible that by tilting the rectangle, so to speak, the maximized area would be obtained, or if it was in the question's best interest to assume a rectangle with sides parallel to the x-axis.
 
  • #4
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
774
Actually, this is an extension on first-time calculus. Our teacher was suggesting if it was possible that by tilting the rectangle, so to speak, the maximized area would be obtained, or if it was in the question's best interest to assume a rectangle with sides parallel to the x-axis.

I didn't know a question had a "best interest" :smile:

The difficulty of having that problem in a first course is that it would be an optimization problem in two variables. If you haven't had that yet, it would presumably be beyond your abilities. Still, it might be an interesting problem given you had the background.
 

Suggested for: Optimization of a rectangle's area in two parabolas

  • Last Post
Replies
2
Views
1K
Replies
1
Views
1K
Replies
4
Views
1K
  • Last Post
Replies
3
Views
7K
Replies
3
Views
1K
Replies
24
Views
3K
  • Last Post
Replies
3
Views
5K
Replies
1
Views
2K
  • Last Post
Replies
7
Views
9K
Replies
7
Views
18K
Top