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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    
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re: solution | Comment 2 of 4 |
(In reply to solution by Daniel)

Does not

(4/3)k^3+k+(1/4)k^-1+(1/48)*k^(-3)

give 1.333333...

when k = 1/2 ?

and this is less than the 1.36797 quoted as a minimum.


  Posted by Charlie on 2009-12-02 12:43:05
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