# PBL Pathways

##### Content Area

Area, left and right sums, fundamental theorem of calculus

##### Time Frame

2 to 3 weeks with mini-lectures

November 3, 2010

##### Keywords

Area, fundamental theorem of calculus

#### Project Title

Total Cost to Produce the Turbo Blender

#### Author

David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

#### Abstract

In this project, students are given values for the marginal cost function and asked to find the total cost of producing a specified number of turbo blenders.

#### Project Content

Project Letter - DOC | PDF

Project Letter 2 - DOC | PDF

#### Scaffolding Resources

Handout: Left and Right Hand Sums - DOC | PDF

#### Notes

I use this project to teach how derivative information (marginal cost) can be converted to antiderivative information (total cost). This can be done several ways. If left and right hand sums are used, students need to struggle with the last rectangle since it spans from 600 to 650 + L. This means they need to estimate the marginal cost at 650 + L. Another approach is to estimate the marginal cost function using regression and then utilize the Fundamental Theorem of Calculus to find the total cost.

Project Letter 2 uses different data and different production levels.