We're to look at this graph and figure out the answers to the following problems. So we want to estimate the rate of temperature at the time 7:00 AM. So if we look at this 7:00 AM is right here and we can see it's a positive slope and we're going up, oh, I don't know, approximately 4 when we're going over two, rough estimate. So up four and over two would be two. So when we look at our four possible answers, we're going to look for the one that's closest to two. And in this case, 1.3. When we look at 9:00 AM here, we're going to go positive slope again. And if I went up five, I'd go over three. So once again, I'm looking for the positive slope that would be closest to 5 thirds, approximately 1.7. These are rough, rough estimates. What happens at two? When I look at 2 here, it's still a positive slope. Now I'm going up a very little and over more. So if I'm going up a little bit over more, I'm looking for a positive slope that's going to be relatively small. So .9. Which of the following is the rate of temperature change at 4:00 PM? So if I come into four, I can see that this is a negative slope and the negative slope is going down some and over some, but it's not real steep, so it's going to be the 1.4. The next question says at what time does the temperature increase most rapidly? So we're looking for a value with the biggest slope decrease most rapidly. Then we're looking for the value with the biggest negative slope. And what is the rate for each of these times? So when we're looking here and we're looking for a really, really fast positive slope, looks like right about in here would be our fast positive, which would be at 11 and our negative is going to be over here, which would be about 6 and positive slope here. So one point 9:00-ish and negative slope here 4.5. Once again, rough estimates. Now when we're finding the graph of the derivative, what we're really asking is what's the slope? So from zero all the way to 9, our slopes are positive, IE the Y values or the derivative are positive. So when I look at these graphs, I need the 0 to 9 to have Y values that are positive, Y values that are positive, so it could be B or D At this nine we have a horizontal tangent so our slope is 0. So our Y value for the derivative graph would have to be 0 at 9:00. And then from 9 on to 12 the slope is negative. So I need the Y values in the graph to be negatives. So our graph choice would be B.