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 ycoordinate 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 ycoordinate where
the curve has a slope of zero.
 There is a minimum at Point
D. This point has the lowest ycoordinate 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.