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Topic: [ap-calculus] Mean Value Theorem
Replies: 2   Last Post: Jul 28, 2012 4:32 PM

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Jeff Stuart

Posts: 1,086
Registered: 12/6/04
Re: [ap-calculus] Mean Value Theorem
Posted: Jul 26, 2012 10:31 PM
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Let f(x) be a nonconstant, linear function on the interval [a,b] where a
< b. Then one of f(a) and f(b) will be the unique local and absolute
maximum and one will be the unique local and absolute minimum (if your
definition of local extremum allows for a one-sided extremum). Note
that every point between a and b qualifies as one of the c's whose
existence is guaranteed by the MVT. If we now consider the constant
function on [a,b], then every point between a and b qualifies as all of
the following: one of the c's as well as a local max, a local min, an
absolute max, a local min, and an absolute min.

Professor Jeff Stuart, Chair
Department of Mathematics
Pacific Lutheran University
Tacoma, WA 98447 USA
(253) 535 - 7403

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