Graph the derivative of the function graphed on the right. So what it's really asking us to do is to think about whether the derivative is +0 or negative. So when we look at this graph, we're increasing on this interval or our graph is going up. So our derivative value would be positive. So we're looking for a graph where it starts with the derivative being positive, the derivative being positive, the derivative being positive. We then have a derivative value right here where it's zero. So we need to be crossing the axis. We need to have a derivative point of 0. From there we have this where we're going down or the derivative is negative. So if we're graphing the derivative, we need the Y values to be negative. We need the Y values to be negative, we need the Y values to be negative. At this location, we have another zero, so we might have this one as a zero. This one, we don't come back UPS. There's no zero there. This one has a 0. Then we need to have our Y values being positive because the slope of this graph is going up. So we have Y values that are positive, we have Y values that are positive. Then once again, we're going to have zero at this top piece, so we need another zero, and we need another zero, and then our graph is going down again. If it's going down, we know that our Y values are going to be negative. So it looks like it could be A or D So the next thing we need to do is we need to pay attention to where this graph is. Well, one of the zeros here will be to the left of the Y axis. A second zero would be to the left of the Y axis, but this one would be to the right of the Y axis. When we look over here, all three zeros were to the left of the Y axis. When we look here, we have two to the left and one to the right. So our answer has to be D. So when we're graphing the derivative, we're really saying, is the slope positive? If the slope is positive, we're above the X axis, or our YS are positive. Is the slope 0? If the slope is 0, we're right on the X axis. That's where y = 0. The slope is negative. We're below the FX, the X axis.