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Suppose $ N $ is the number of people in the United States who travel by car to another state for a vacation this year when the average price of gasoline is $ p $ dollars per gallon. Do you expect $ dN/dp $ to be positive or negative? Explain.

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A negative divided by a positive will equal a negative.

01:56

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Campbell University

Oregon State University

Baylor University

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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In this problem, we have n the variable end is the number of people traveling by car on vacation. T is the price in dollars per gallon of gas? And we wanted to determine if this derivative would be positive or negative. Uh So how does, um uh and a number of people traveling by car change with respect to a change in the price of gas? Well as gas increases, the number of people traveling by car is going to decrease, because if it's more expensive to travel, because it costs more for gas, uh not as many people are going to decide to travel. So if the price of gas is increasing, the number of people traveling is decreasing. So you can think of this as a negative amount over a positive amount. And so this derivative Is going to be negative or less than zero.

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