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.

(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