Bunny hops: using multiplicities of zeroes in calculus for graphing

Abstract

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students’ pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.

Keywords:

• calculus
• graphing
• zeroes
• multiplicities
• college algebra