All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
A Normal and a Parabola (Posted on 2009-12-02) Difficulty: 3 of 5
Choose any point (k,k^2) with k>0 on the parabola y=x^2. Draw the normal line to the parabola at that point. Then there is a closed region defined by the parabola and the line. Find the value of k so the area of the region is minimized.

Note: A normal line is a line perpendicular to a tangent at the point of tangency.

See The Solution Submitted by Brian Smith    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: solution error found | Comment 3 of 4 |
(In reply to solution by Daniel)

You err


and this is minimized when
4k^6+   k^4    -(1/4)k^2-(1/16)=0                             *16
64k^6+  k^4  -4k^2-1=0

while multiplying by 16 you have left one member  (k^4) unchanged

therefore the rest is wrong , although your solution followed the right track.

Please correct and explain way of solving - I suggest substitutingb  m=k^2 to get a cubic equation.

  Posted by Ady TZIDON on 2009-12-02 14:43:34
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information