In this pair / small group activity, students apply what they know about extrema and inflection. Students are given a description of four functions' increasing / decreasing behavior and must determine which descriptions* of each function's first and second derivatives must be true.
* Example descriptions on the "answer cards":
f ’’ (x) is negative on (-2, 7)
f ’ (-2) = 0 and f ’’ (-2) < 0
f has a relative min at x = 7
f ’ (x) changes from neg to pos at x = 7
The file includes instructions and an answer key. Each card has a letter on it, so teachers can quickly check answers by checking that the sets spell a given word.