## Function - Rate of Change Question

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
earthworks1975
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### Function - Rate of Change Question

Good evening all!

I having difficulty with the this problem: f(x)=x2 from x1=3 to x2=6. I got the answer 9 but I'm not sure where to calculate the x2-2x....or even HOW to incorporate it into the problem.

Any help would be greatly appreciated.

Melanie

stapel_eliz
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I having difficulty with the this problem: f(x)=x2 from x1=3 to x2=6.
What were the instructions? What are you supposed to be doing with this function over the specified interval?
How did you get this? What did you do?
...but I'm not sure where to calculate the x2-2x....or even HOW to incorporate it into the problem.
Why would this be part of the exercise? What does it have to do with the original function or interval?

earthworks1975
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### Re: Function - Rate of Change Question

Thanks for your reply! I apologize for not being thorough. I see from my original post that I screwed up typing the problem. The problem is f(x)=x2-2x from x1=3 to x2=6. Sorry!

1. The instructions to the problem state: Find the average rate of change of the function x1 to x2.

2. I arrived at 9 by substituting 6 and 3 for the x variables. f(6)-f(3)/6-3. Then, I multiplied and substracted, leaving me with 27/3....which left me with 9. But, I did not know what to do with the x2-2x part.

3. In this section, we were doing parallel/perp slope, using point slope and slope intercept forms. The latter part of this section was rate of change but neither our instructor nor the book shows how to do rate of change with the x2-2x part.

Thanks for your help! I'm 39 years old and trying desperately to get through this class so I can then get into Stats....and then finally graduate. I should have taken these math classes 20 years ago instead of waiting. Lol. My mind hasn't gotten any better at "mathing" but my patience and persistence has, at least.

Thanks!
Melanie

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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Thanks for your reply! I apologize for not being thorough. I see from my original post that I screwed up typing the problem. The problem is f(x)=x2-2x from x1=3 to x2=6. Sorry!

1. The instructions to the problem state: Find the average rate of change of the function x1 to x2.
So follow the algorithm they gave you: plug the interval endpoints (the x-values) into the formula for f(x), find the corresponding y-values, and find the slope of the line through these two (x, y) points.
I did not know what to do with the x2-2x part.
I'm sorry, but I don't understand what this means. How did you find the values for f(x) if you didn't use the formula, x^2 - 2x, for f(x)?

Alan51q
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### Re: Function - Rate of Change Question

If the equation is f(x)=x2-2x, then the point for x1=3 should be (3,3) i.e. f(3)=32-2(3) =9-6=3, so (3,3)

and x2=6 should be (6,24) I believe. That being the case,

m= (24-3)/(6-3) = 21/3 = 7

If I'm correct, then the rate of change is 7.

Unless I'm misunderstanding something.