These 24 cards are separated into 6 sets of four cards.
Set 1 (Cards 1-4): Explain why the EVT does or does not guarantee the existence of an absolute maximum and minimum on the given domain
Set 2 (Cards 5-8): Locate all local and global extrema on the graph.
Set 3 (Cards 9-12): Find critical values graphically and analytically.
Set 4 (Cards 13-16): Given a function, find all critical values analytically.
Set 5 (Cards 17-20): Find all absolute extrema.
Set 6 (Cards 21-24): Rolle’s Theorem - Finding locations where f ’(c)=0 and deciding if Rolle’s Theorem can be applied
All the cards require the students to understand the need for a function to be continuous on a closed interval to apply the extreme value theorem. Using a graph, students will be asked to identify local and global extrema. Students will find critical
values both graphically and analytically. On other cards students will find the absolute extrema. The last set of cards has students consider whether Rolle’s Theorem can or cannot be applied to the described function. Students will asked to explain their reasoning on many of the cards.
3. The cards can be set up in 6 stations and students can be asked to complete
either 1, 2, 3, or 4 cards in the set.