Your monthly car payment in dollars is P = f(Po,t, r), where $Po 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 OP/at positive or negative? negative v Suppose that your bank tells you that the magnitude of aP/dt is 35. What are the units of this value? (For this problem, write our your units in full, writing dollars for S, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) (b) Is aP/Or positive or negative? positive Suppose that your bank tells you that the magnitude of aP/ar 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.

Your monthly car payment in dollars is P = f(Po,t, r), where $Po 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 OP/at positive or negative? negative v Suppose that your bank tells you that the magnitude of aP/dt is 35. What are the units of this value? (For this problem, write our your units in full, writing dollars for S, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) (b) Is aP/Or positive or negative? positive Suppose that your bank tells you that the magnitude of aP/ar 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.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Your monthly car payment in dollars is P = f(Po,t, r), where $Po 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 ðP/dt positive or negative? negative v
Suppose that your bank tells you that the magnitude of aP/dt is 35.
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 ðP/ðr positive or negative? positive v
Suppose that your bank tells you that the magnitude of aP/ar 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.

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Derivative of a function basically determines that rate of change of that function with respect to time.

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