   Chapter 7.4, Problem 72E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Think About It Let N be the number of applicants to a university, p the charge for food and housing at the university, and t the tuition. Suppose that N is a function of p and t such that ∂ N / ∂ p <   0  and  ∂ N / ∂ t <   0 . What information is gained by noticing that both partials are negative?

To determine

The reason that both partial derivative Np andNt are negative if N denotes number of applicants in the university, p denotes charge for food and housing and t denotes the tuition.

Explanation

Given Information:

Let N is a function of p and t where N denotes number of applicants in the university, p denotes charge for food and housing and t denotes the tuition such that Np<0 andNt<0

Calculation:

Consider the provided information,

Let N is a function of p and t where N denotes number of applicants in the university, p denotes charge for food and housing and t denotes the tuition such that Np<0 andNt<0

Suppose, f(x)=y is the real valued function and the negative derivative of f(x) represents the function is decreasing.

It means there is inverse relationship between y and x as we increase the value of  x then the value of f(x) would be decrease

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