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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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2 replies to this topic

### #1 bonanova

bonanova

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.

• -1
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #2 m00li

m00li

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Posted 27 April 2014 - 08:57 PM   Best Answer

Spoiler for 2 approaches

• 0

### #3 bonanova

bonanova

bonanova

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Posted 28 April 2014 - 03:59 AM

Nice job m00li.