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Find the average rate of change of $y$ with respect to $x$ on the given interval.$$y=3 x^{2}-7 x-5 ;[3,6]$$

$$20$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

Derivatives

Campbell University

Idaho State 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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so to find the average rate of change would take the change in y over change in X, which is why to minus y one over x two minus X one. So here are our x one and X two variables three and six, respectively. So we plug and chug each of the X values into the function to be able to get our y one and Y two. So after you plug in three into the X, you get why one is equal to one, and then after plugging six into the X into the above equation you get y two is equal to 61. So if you plug these two back into your average rate of change equation, you get 61 minus one over you. Take these two x variables and take the difference. So six minus three, which is 20 over or sorry, 60/3 or 20 and that is your average rate of change.

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