Detailed Solutions to Initial Practice
Unit 3: Determining Whether the Slope of a Curve is Positive, Negative, or Zero

For each point on the curves below, identify whether the slope is positive, negative, or zero. Also, identify which are the maximum and minimum points (if any).

The tangent lines have been drawn at each point so that you can see the slope of those lines.
 In graph (a) Slope of the tangent line at point A is negative, Slope of the tangent line at points C and D are both positive, and Slope of the tangent line at point B is zero. Point B is the minimum point. It is the point with the lowest y-coordinate where the curve has a slope of zero.
 In graph (b) Slope of the tangent line at point C is negative. Slope of the tangent line at points A and E are both positive. Slope of the tangent line at points B and D are zero. There is a maximum at point B. This point has the highest y-coordinate where the curve has a slope of zero. There is a minimum at Point D. This point has the lowest y-coordinate where the curve has a slope of zero.

If you had problems with this practice, review this unit. If you feel you need to review slopes of straight lines, you should read through the unit on slopes in the previous tutorial in this series. Then go on to the additional practice for this unit below.