RUME 26
2024
Omaha, Nebraska
An Exploratory Study of Students’ Understanding of Graphical Optimization in a Cost Minimization Context
Page: 1273
This study reports on first-semester calculus students’ reasoning about a univariate optimization problem that involves finding the production level at which the cost per yard is minimized when given the graph of a function that represents the relationship between the cost per yard and the number of yards produced by a factory. Analysis of verbal responses and work written by four students when solving the problem revealed that determining the production level at which the cost per yard is minimized was straightforward for all the students. However, explaining how this production level is related to the first derivative of the given function was problematic for most of the students.