Your monthly car payment in dollars is P = f(P_0, t, r), where $P_0 is the amount you borrowed, t is the number of months it takes to pay off the loan, and r percent is the interest rate.
a. Is dP/dt positive or negative?
Suppose that your bank tells you that the magnitude of dP/dt is 20.
What are the units of this value?
(For this problem, write our your units in full, writing dollars for $, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.)
b. Is dP/dr positive or negative?
Suppose that your bank tells you that the magnitude of dP/dr is 5.
What are the units of this value?
(For this problem, write our your units in full, writing dollars for $, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.)
For both parts of this problem, be sure you can explain what the practical meanings of the partial derivatives are.