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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(2): solution error found Comment 4 of 4 |
(In reply to re: solution error found by Ady TZIDON)

thanks for pointing out my mistake after correcting my error the derivative factored quite nicely to give the solution k=1/2 that Charlie hinted at in his reply.
  Posted by Daniel on 2009-12-02 22:08:16

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