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 .
, 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
Download paper from here.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395