IJPAM: Volume 75, No. 3 (2012)
Penn State Brandywine
25, Yearsley Mill Rd.
Media, PA 19063, USA
Abstract. Let be a differentiable function on the real line, and let
all points not on the graph of
. We say that the illumination index of
, denoted by
, is
if there are
distinct tangents to the graph of
which pass through
. In section 2
we prove results about the illumination index of
with
on
. In particular, suppose that
and
are distinct oblique asymptotes of
and let
. If
, then
. If
and
, then
.
Finally, if
, then
. We also show that any point below the graph of a convex rational function
or exponential polynomial must have illumination index equal to
. In
section 3 we also prove results about the illumination index of polynomials.
Received: July 28, 2011
AMS Subject Classification: 26A06
Key Words and Phrases: tangent line, oblique asymptote, illumination index
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 3