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Find the average rate of change of $y$ with respect to $x$ on the given interval.$y=m x+b ; \quad\left[x_{1}, x_{2}\right],$ interpret this answer.

$$m \sec 14$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

Derivatives

Oregon State University

Baylor University

Boston College

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Find the average rate of c…

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mhm. So to find the average rate of change you have your what is an average you take your results of or your final result minus the initial result over your final input minus the initial input. So here we have y two. That is why one which basically why in this linear function is a function of X because you have X and as the variable here so you can look at as f of X two, which is your final minus your initial over. Sure final variable rear initial variable. So what that means if you look at the graph, y equals MX plus B. It's just a linear slope, right? So let's say you have this point, which is your ex initial at this point as your ex final. That's supposed to be it too. And you would go over here and you get this as your y initial and your wife Fine final. So between this point here, what? How much is it changing? And that's what this function gives you. The average rate of change is about how much does your why change as your exchanges

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