Problem

Find the average rate of change for each function…

02:17

Problem 3 Easy Difficulty

Find the average rate of change for each function over the given interval.
$$y=-3 x^{3}+2 x^{2}-4 x+1 \quad \text { between } x=-2 \text { and } x=1$$

Answer

-15

Related Courses

Calculus 1 / AB

Finite Mathematics and Calculus with Applications

Chapter 11

The Derivative

Section 3

Rates of Change

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 11

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Video Transcript

they want to find the average rate of change for the function. Why is it to negative three X cubed plus two Expert minus four x plus one between Mexico donated to and X is equal to one. So the average rate of change is just a fancy way of saying find the slope of the secret line that goes between them between these two points. So, uh, that means are a is going to be negative to be is one. And you could do this in either order. Doesn't matter, just like for the slope of the line. When we did it, as long as we just had two points, that's all that mattered. So let's go ahead and figure these out, though. So if we call f of X, why than f one is going to be equal to so would have negative three plus two minus four plus one and adding these up, it looks like that would just be negative for then, when we plug in negative too, we're gonna end up with negative three times negative eight plus two times or minus four times negative two plus one and then simplifying this down. We'd have 24 while state plus eight plus one and adding, these of it looks like would get 41. So now let's go out and plug everything in. So we have f b. So that's gonna be up for once. We have negative four minus f of A, which is 41 then this is going to be all over one minus negative too. So these negatives right here will counts out with each other and then we'd have negative 45/3, which is equal to negative 15 So this would be our average rate of change on that interval.

Get More Help with this Textbook