Describing derivatives in practical terms

AI Thread Summary
The discussion focuses on determining the units and sign of the derivative C'(r) for the total cost of a car loan based on the interest rate r. C'(r) is expressed as dC/dr, leading to the conclusion that its units are dollars per percentage point of interest. Participants clarify that the sign of C'(r) indicates whether the cost increases or decreases with changes in the interest rate. Additionally, r is identified as a percentage. The conversation emphasizes the need for clarity in interpreting these financial derivatives.
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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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