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The "aha!" problems - 3 minimum areas


Best Answer m00li, 27 April 2014 - 08:57 PM

Spoiler for 2 approaches
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#1 bonanova

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Posted 27 April 2014 - 07:27 AM

A while back I started a series of puzzles that seem difficult but

have not-so-difficult answers. I can't find any of them, so I don't

know how many exist. There must have been at least two, so I'll

number this one 3. Have fun.

 

A monotonic increasing function f (x) is cut above and below by horizontal lines that intersect it at  f (x1) and f (x2).

A vertical line is drawn through a point on the curve (black dot) between x1 and x2.

The curve and the lines define the green and red areas shown on the figure.

 

You are to find the point on the curve that minimizes the sum of these areas.

jp21.gif


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 m00li

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Posted 27 April 2014 - 08:57 PM   Best Answer

Spoiler for 2 approaches

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#3 bonanova

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Posted 28 April 2014 - 03:59 AM

Nice job m00li.
It is the first of your two answers that I had in mind.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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