Question

Find the average rate of change of f(x)=x^3-3x+1
(a) From -5 to -3
(b) From -2 to 2
(c) From 2 to 3

Answer 1

you need to find the ordered pairs

find f(-5) and f(-3)

so the average rate of change is

\[\frac{f(-5) - f(-3)}{-5 - (-3)}\]

you are really just finding the slope of the line between the 2 points

Answer 2

Here's a graph of what you're doing (first part only):

Answer 3

Okay thanks!!

Answer 4

okay that wasn't the right answer, but thanks!!!

Answer 5

what wasn't the right answer?

Answer 6

I just don't know how to do the problem that's all, getting frustrated.... Thanks!!!

Answer 7

well, @campbell_st did tell you what to do. I'll try explaining it again.

To find the average rate of change between two points on the curve, you need to find the (x,y) values for the two points. In the first part, they are (-5,f(-5)) and (-3,f(-3)). Then you plug those values into the formula for the slope of a line passing through the two points:
\[m = \frac{y_2-y_1}{x_2-x_1}\]and \(m\) is your average rate of change.

For the first part, that would be
\[m = \frac{f(-5) - f(-3)}{-5-(-3)} = \frac{ ((-5)^3-3(-5)+1)) - ((-3)^3-3(-3)+1))
}{-2} \]\[=\frac{(-125+15+1)-(-27+9+1)}{-2} =\frac{ -109-(-17)}{-2} = \frac{-92}{-2} =46\]

Answer 8

Now you repeat the drill for the other two sets of points. If you post your answers, I'll check them for you.

Answer 9

okay......

Answer 10

Never mind whpalmer, I'm just not getting it.. when it comes to math, you need a blended environment, meaning a classroom setting... I'm more of a visual learner, and math is my worst subjects.... I thank you for your time, that you have spent with me... Don't worry about the rest of the problems... Thanx!!!

Answer 11

I'd hate to have you be the first person I couldn't successfully teach.

Answer 12

let's break it down further. do you understand the notion of slope?

Answer 13

(my previous remark was not intended as any sort of slight or judgment — just that I'm willing to work with anyone who wants to learn for as long as it takes)

Answer 14

No you did a very good job trust me, I'm frustrated right now to where I can't think.. Math is a type of subject where you can't spend a long time on, especially on the internet. I'm kind of wore out, that's all... Trust me you did a fine job!!

Answer 15

feel free to send me a message later if you want help with this or anything else.

Answer 16

go outside, take a walk, ride your bike, go for a swim, do something else for a while. breaks are good :-)

Answer 17

okay I will do that... Let me get a bite to eat.. I think that's whats wrong with me:)

Answer 18

Thanks for the advice...... c u soon....