Your monthly car payment in dollars is [math], where $[math] is the amount you borrowed, [math] is the number of months it takes to pay off the loan, and [math] percent is the interest rate.

(a) Is [math] positive or negative?
Suppose that your bank tells you that the magnitude of [math] is 15.
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 [math] positive or negative?
Suppose that your bank tells you that the magnitude of [math] is 25.
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.

Solution: