Using the graph below, answer the following questions. The tangent lines have been drawn at each point on the curve so that you can see the slope of those lines. The questions below can be answered by looking at the tangent lines drawn.

At which points is the slope of the curve positive? Of the labeled points on the curve, none of them are at a point where the slope goes up from left to right. So no labeled point is on a portion of the curve that has a positive slope.

1. At which points is the slope of the curve negative?
   
2. Of the labeled points on the curve, three of them are at a point where the slope goes down The curve is negative at points A, B, & E.
3. What is the slope at point D?
   At point D the tangent line is horizontal. Therefore, the slope of point D is 0 (zero). By the way, the slope of the curve is also zero at point C.
4. Are there any maximum or minimum points in the curve? If so, which point(s) are maximum and minimum.
   • Maximums and minimums occur at points where the slope is zero. There are two of these points in the graph, C and D. The minimum is at point C, and the maximum is at point D.
   • Point C is the point with the lowest y-coordinate with a slope of zero; therefore, it is a minimum point.
   • Point D is the point with the highest y-coordinate where the slope of the curve is zero; therefore, it is a maximum point.

If you feel comfortable with this material, move on to the summary and then complete the review test.

IMPORTANT: If you still do not understand how to identify if the slope of a curve is positive, negative, or zero, or how to determine if a point is a maximum or a minimum, you may need more review than is offered by this book. You may wish to review Book I, Part Two of this series first. Then, if you are still having problems, please speak with your professor for suggestions on how to get help.

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