Re: Increasing and decreasing functions - conflicting authors

"The World Wide Wade" <waderameyxiii@xxxxxxxxxxxxxxxxxxxx> wrote in message
news:waderameyxiii-9B2B90.08191116052006@xxxxxxxxxxxxxxxxxxxxxxxxxxx
In article <yb6dnTGkiZnkUPTZRVn-gg@xxxxxxxxxxx>,
"Colleyville Alan" <nospam@xxxxxxxxxx> wrote:

"William Elliot" <marsh@xxxxxxxxxxxxxxxxxx> wrote in message
news:Pine.BSI.4.58.0605152230580.13100@xxxxxxxxxxxxxxxxxxxx
On Mon, 15 May 2006, Colleyville Alan wrote:

I am starting to read Stewart's Calculus Early Transcendentals (1999
ed.)
for a Calc I class that will begin in a few weeks. In it he talks
about
increasing and decreasing functions and shows the intervals using
closed
interval notation. In my College Algebra text (Beecher, Penna, &
Bittinger), they emphatically state that you need to use open interval
notation when discussing increasing, decreasing, or constant intervals
as
it
is impossible for a point to be increasing and decreasing at the same
time.

How are they using these terms?
Do they distinguish between increasing and strictly increasing?


They do not distinguish. The definition given is:
"A function f is said to be increasing on an open interval l, if for
all
a and b in that interval, a < b implies f(a) < f(b)".
The definitions for decreasing and constant intervals are similar.

They go on to explain:
"In calculus, the slope of a line tangent to the graph of a function
at
a particular point is used to determine whether the function is
increasing,
decreasing, or constant at that point.

And how do they define "increasing at a point"?

They don't define it. This was a College Algebra textbook.


.

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