These 24 cards are separated into six sets of four cards.
• In set 1 a student must explain why the EVT does or does not guarantee the existence of an absolute maximum and minimum on the given domain.
• In set 2 a student must locate all local and global extrema on the graph.
• In set 3 a student must find critical values graphically and analytically.
• In set 4 a student must find all critical values for a function analytically, given an analytical form for the function.
• In set 5 a student must find all absolute extrema for a given function.
• In set 6 a student must use Rolle’s Theorem to find locations where f ’(c)=0 and decide if Rolle’s Theorem can be applied.
Many of the cards require the students to communicate their reasoning. This is a skill all AP students should be developing during their year of calculus.
The questions have been modeled after the way the questions have been asked on recent Advanced Placement exams. This should help prepare your students to answer those questions when the questions appear on the AP test.
• 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.
The task cards can be used in many different ways to differentiate the lesson.
• The cards can be set up in six stations and students can be asked to complete either 1, 2, 3, or 4 cards in the set.
• The students can be placed into four groups and each group can be given one card from each set. The students could be required to make a presentation of all six of their cards to the rest of the students after they have solved the questions.
• After students have solved several problems from each set they could be asked to explain their solution to another student. This second student could help evaluate the first student’s understanding of the EVT concept.