Linearity and Concavity

Date: 12/07/2003 at 17:32:44
From: Ted 
Subject: Calculus Question

Why does a linear function have no concavity?

Date: 12/07/2003 at 18:26:09
From: Doctor Schwa
Subject: Re: Calculus Question

Hi Ted,

Concavity tells you whether a function is curving upward (increasing
slope) or downward (decreasing slope).  Since a line has constant 
slope, it's not concave up or down.

Another way to say it is that concavity tells you whether the second 
derivative is positive or negative, and a line has second derivative 
zero.

Does that help?

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/08/2003 at 08:23:21
From: Ted 
Subject: Thank you (Calculus Question)

Thank you so much!  That clears everything up.