Newsgroups: sci.math
From: m.ward@csuohio.edu (Michael Ward)
Subject: Optimization Question
Date: Thu, 16 Feb 1995 15:51:16 GMT

    I need a little help with the following problem.  I am a student currently 
enrolled in a calculus class.  My teacher has offered extra credit to any who 
solve the following problem.  He also encourages use of any resources 
available so I put it to you, fellow net junkies.

    Given a function f defined on [0,1], for which of its non-vertical tangent 
lines T is the area between f and T minimal?

   It is required that I solve this problem for three different non-linear 
functions of my choosing, but each function must be from a different class of 
functions (i.e. polynomial, radical, rational, trigonometric, exponential, 
logarithmic).  It is strongly suggested that I stick to functions whose 
concavity does not change on the interval [0,1].  The final result, hopefully, 
will be a function that will minimize the area between any function f and its 
non-vertical tangent lines T.

    I have spent a good deal of time on this problem and have made progress.  
I would greatly appreciate any help offered.

Thanks,
Michael Ward
m.ward@csuohio.edu