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Find the average rate of change of $y$ with respect to $x$ on the given interval.$y=3 x+2(a)[0,1] ;(b)[3,5] ;(c)\left[x_{1}, x_{2}\right]$ interpret this answer

Each answer is $3,$ the rate is the slope.

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

Derivatives

Missouri State University

Campbell University

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.

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 first you want to find to find the average rate of change of why, With respect to X, we use the formula for the average change, which is ask of X one or X two minus F of X one over X two Nice X one. So that's actually your answer for number C would be this equation. So for part A, you have X two equals one so f of one. You plug and chug one in here and you get five minus zero or F m zero, which would be to over one minus zero. So your average rate of change is three for me? Yeah, you have three and five. So you plug in will use a different colour three and two x and five and two X. So if you plug in five and two X, you get 17. And then if you plug three into eggs, you get 11 and then five minus three, which equals three. And so far for part C, we already have the equation over here. Let me actually use a different color the equation over here and you can see that these two intervals were three. And if you look at the equation itself. It is linear, which means that it has a constant rate of change since it's constantly going up like this. So the rate is constant, which means for any value of X one and x two, the rate of change will be three.

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