Describing derivatives in practical terms

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Homework Help Overview

The discussion revolves around understanding the derivative of a cost function, C(r), related to a car loan with respect to the interest rate, r. Participants are exploring the implications of this derivative, particularly its units and sign.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to determine the units of C'(r) and questioning whether it can be expressed as dollars per percent interest. There is also uncertainty regarding the meaning of "What is its sign?" and whether it refers to being positive, negative, or zero.

Discussion Status

The discussion is ongoing, with participants actively questioning the units of the derivative and seeking clarification on its sign. Some guidance has been offered regarding the interpretation of the derivative's units, but no consensus has been reached.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for a complete understanding of the derivative's implications.

madgab89
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Homework Statement



Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%. What are the units of C '(r)? What are the units of C'(r)? What is its sign?

Homework Equations


C'(r)=dC/dr


The Attempt at a Solution



So, I figured:

C'(r) = dC/dr
Which is dollars over interest rate(?)...which seems kinda awkward to me. I'm wondering if there's a better solution for what the units of C'(r) would be. (dollars per percent interest?)

And I'm not sure what is meant by "What is it's sign"?
 
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What are the units of r?

"What is it's sign" means is it positive or negative ... or zero.
 
r is a %
 
Okay. So the units of C/r would be ... ?
 

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