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? The number of applicants will only decrease regardless of change in either p or t.The number of applicants is unaffected by change since both derivatives have the same sign. The number of applicants decreases if both p and t are constant.The number of applicants increases only if both p and t increase.The number of applicants decreases if either p or t increase while the other holds constant.
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? The number of applicants will only decrease regardless of change in either p or t.The number of applicants is unaffected by change since both derivatives have the same sign. The number of applicants decreases if both p and t are constant.The number of applicants increases only if both p and t increase.The number of applicants decreases if either p or t increase while the other holds constant.
Chapter3: Graphs And Functions
Section3.5: Relations And Functions
Problem 335E: Is every relation a function? Is every function a relation?
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Question
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 |
and
| ∂N |
| ∂t |
What information is gained by noticing that both partials are negative?
The number of applicants will only decrease regardless of change in either p or t.The number of applicants is unaffected by change since both derivatives have the same sign. The number of applicants decreases if both p and t are constant.The number of applicants increases only if both p and t increase.The number of applicants decreases if either p or t increase while the other holds constant.
Transcribed Image Text: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
<O and
< 0. What information is gained by noticing that both partials are negative?
O The number of applicants will only decrease regardless of change in either p or t.
O The number of applicants is unaffected by change since both derivatives have the same sign.
O The number of applicants decreases if both p and t are constant.
The number of applicants increases only if both p and t increase.
O The number of applicants decreases if either p or t increase while the other holds constant.
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