Make-up Reflection #3

Graph Interpretation


Every AP exam will include at least one graph on it's short answer section that requires the test-taker to interpret certain requirements from it in order to receive credit for that question.

Interpreting a graph is very easy but in order to do it properly one must understand certain properties.

1.  If the original graph is increasing, the slope is positive.
2.  If the original graph is decreasing, the slope is negative.
3.  An interval with a positive slope on the first derivative means that there is a downward concavity on that interval in the second derivative.
4.  An interval with a negative slope on the first derivative means that there is an upward concavity on that interval in the second derivative.
5.  Upward concavity (bowl-shaped) is positive.
6.  Downward concavity (umbrella-shaped) is negative.
7.  There is a horizontal tangent where the slope=0 on the original graph.
8.  Wherever there is a horizontal slope there is either a maximum or a minimum value.
9.  A x intercept on the first derivative is either a maximum of a minimum on the original graph.