Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%. What is the practical meaning of C'(r)?
What is the units?
2006-09-17 08:13:06 · 4 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
is the units dollar/percent? and is the sign of C'(r) negative?
my interpretation to this is the amount of money we have to pay at when the interest rate is at r%.
Am i right?
2006-09-17 08:24:37 · update #1
change in cost with respect to the interest rate, units would be the dollar/rate.
Practical meaning, it just give the slope of the change in cost/rate. If the slope is postive, the cost is increasing for increase in rate near that interval. It it is zero, you have either reached a local max or min value of cost, or the cost is constant over that interval (have to look at the curve),ect.
2006-09-17 08:49:38 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Very likely the units are dollars per month (or year), depending on if you take the APR and spit it up into the monthly equivalent rates. The first derivative with respect to time is simply the rate at which you pay off the loan.
2006-09-17 08:33:16 · answer #2 · answered by oldprof 7 · 0⤊ 0⤋
A PhD in business administration? What's next: a PhD in typing?
The derivative of a function is the rate of change of a function with respect to the independent variable. In this case, the function is a cost (in whatever currency you use) and the independent variable is a number, which stands for an interest rate. So the units would be dollars, that is, dollars per point of interest.
2006-09-17 08:44:57 · answer #3 · answered by Benjamin N 4 · 0⤊ 1⤋
C'(r) would be the rate at which your cost increases for when your rate increases.
Units would be dollars
2006-09-17 08:19:31 · answer #4 · answered by Demiurge42 7 · 0⤊ 0⤋