Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Explain why a decreasing demand function has a negative elasticity function.

Calculus 1 / AB

Chapter 3

Derivatives

Section 6

Derivatives as Rates of Change

Differentiation

Oregon State University

Baylor University

University of Nottingham

Idaho State University

Lectures

04:40

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

04:00

Why does the demand curve …

01:43

Why does a reduction in ag…

04:29

What are the factors that …

07:24

Explain the law of demand.…

01:46

How does demand elasticity…

How is elasticity of suppl…

00:24

Explain how the elasticity…

So for this problem, we're gonna be talking about elasticity functions. All right, here is what the elasticity function is and because we know that the demand function is decreasing, we know that to change in demand of the change in price because the demand function is a function of price. We know that this is going to be some negative negative numbers of negative constant right, And we also know that price and demand are always positive. So if price and demand are always positive and this number right here is negative, we have a negative C times some positive number. We know that the elasticity function itself, which is you have P is going to be some negative constant se que So that's how we know that when the demand function is negative, we can also say that the elasticity function is negative.

View More Answers From This Book

Find Another Textbook

00:15

Fill in the blanks. The derivative of $f(g(x))$ equals $f^{\prime}$ evaluate…

03:51

Derivatives Find and simplify the derivative of the following functions.…

01:36

01:09

Derivatives Find the derivative of the following functions. See Example 2 of…

01:24

Calculate the derivative of the following functions.$$y=\cos 5 t$$

06:36

The magnitude of the gravitational force between two objects of mass $M$ and…

02:48

Derivatives from limits The following limits represent $f^{\prime}(a)$ for s…

02:12

01:38

Use the following table to find the given derivatives.$$\begin{array}{lc…

01:39

For each of the following composite functions, find an inner function $u=g(x…