Usability of Second Derivative Test. The second derivative test is often most useful when seeking to compute a relative maximum or minimum if a function has a first derivative that is (0) at a particular point. Since the first derivative test is found lacking or fall flat at this point, the point is an inflection point.
Increasing and Decreasing Functions & The First Derivative Test Draw 10 different tangent lines to the graph below: What is true about the slopes of a graph when the function increases(y-values increase as x-values increase left to right)? What is true about the slopes of a graph when the function decreases(y-values decrease as x-values increase left to right)?