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- anonymous

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- jamiebookeater

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- anonymous

Well, the average rate of change between two points is simply the slope between them. So I assume you know slope to be determined by \[\frac{ y_{2} - y_{1} }{ x_{2}-x_{1} }\]
So in the first statement, if the average rate of change, the slope, is 0, what must be true about
\[\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }\]?

- anonymous

I don't know xc ... maybe between -3 and 3 there are solutions?

- anonymous

Well, if the average rate of change is 0 then the slope is 0. Which means
\[\frac{ y_{2} - y_{1} }{ x_{2}-x_{1} } = 0\]
Basically, how can we make that fraction for slope =0?

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## More answers

- anonymous

would the demominaters be -3 and 3? 3-(-3)

- anonymous

Yes, they would be. So you would have \[\frac{ y_{2}-y_{1} }{ 6 } = 0\] So what does that say about y_2 and y_1?

- anonymous

That there not identified yet?

- misty1212

|dw:1433728163730:dw|

- anonymous

Sorry, not trying to tease or anything, just wanted you to see it. Well, the only way a fraction can be 0 is if the numerator is 0. Which means
\(y_{2} - y_{1} = 0\)
\(y_{1} = y_{2}\)
The idea is that the y coordinate of both points has to be the same in order for the average rate of change to be 0. That make sense?

- anonymous

Kinda, it makes the reasoning for why its 0

- anonymous

would that explain tuckers part on why he's correct? or is there more to tuckers reasoning :o

- anonymous

Yeah, exactly. So the first person is essentialy saying the y-coordinates for both points are the same. It doesnt matter what they are, we just want them to be the same. So, for example, lets say our y-value is 0. So we would have the points (-3,0) and (3,0).

- anonymous

As for the 2nd person, considering the graph between -3 and 3 we know it'll go up and then back down. But at the same time, we also want the graph to start and begin at the same y-value. So we want something like this.
|dw:1433728476305:dw|
So, the best example of how this is possible is if the graph is a parabola. But really, any continuous function that has the same y-coordinate at x = -3 and x = 3 and is not a line will make them both correct.

- anonymous

Ok! That makes since, and yea i thought it would be a parabola, thanks again! cx xD

- anonymous

Well, I guess it also has to be going up in between -3 and 3, lol. So I guess it cant be EVERYTHING with x-intercepts at -3 and 3, but you get the idea.

- anonymous

Yea lol, thats all i think of when i hear " up and down", and is it ok if i write out the answers and you read to see if it souds right?

- anonymous

Okay.

- anonymous

* Tucker says that for the function, between x = -3 and x = 3, the average rate of change is 0* Here Tucker says that between -3 and 3 x coordinates that the average rate of change is 0.. the slope is y2−y1/x2−x1 and if you plug in the x coordinates you get y2−y1/6=0.... whats true is that the x-coordinates are -3 and 3, whats true about y is y2−y1=0 so y1=y2, the y coordinate of both points has to be the same in order for the average rate of change to be 0

- anonymous

sorry that took forever, but thats tuckers reasoning

- anonymous

It doesnt need to be that wordy, that was just me trying to explain the idea :P Really, all you need to say is something like this: "Tucker can be correct as long as the average of change is 0. As in the slope between the points (-3,y1) and (3,y2) is 0. This is only true if y1 = y2."
I dont think you really need to go into any more detail than that. I would think any detail left out from that is stuff youre assumed to know and dont really need to explain.

- anonymous

Ok lol, yea i was writing it like " wait... should i include this O.o" lol and thanks! ill do the other person, and less wordy lol cx

- anonymous

Yeah, pretty much any minimal conditions that would make the statement true :P In the end, we dont even care about the x-coordinates. The x-coordinates could be anything, but the fact that we know the rate of change has to be 0 just tells us the y-coordinates have to be equal.

- anonymous

Karly is correct also because if you draw a graph between -3 and 3 we know it'll go up and then back down, example parabola

- anonymous

example *a parobla

- anonymous

Well, have to phrase that a little differently, just be careful. The way you phrased it, you said if we draw a graph between -3 and 3. Just by drawing that graph, that doesnt mean it will go up and then down. Just trying to be careful with the wording.
We want to state a condition that makes both of them correct. "Karly claims the goes up through a turning point and then comes back down. This won't contradict Tucker's statement as long as the graph has the same y-coordinate at x = -3 and x = 3. An example where this could easily be true is a parabola."
Not trying to be super picky or mean or anything, I guess Im almost making sure the English is good now and not the math, haha.

- anonymous

No it's ok, I don't want to do bad Cx and thank you so much, your really a big help! cx

- anonymous

You're welcome :)

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