Question

.hjh

Answer 1

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
\[\frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }\]?

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

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?

Answer 6

That there not identified yet?

Answer 7

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?

Answer 8

Kinda, it makes the reasoning for why its 0

Answer 9

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

Answer 10

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).

Answer 11

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.



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.