The Nuffield Foundation provides this activity which can be used to review students' knowledge of the derivatives of quadratic and cubic functions and their graphs. The slideshow provides an introduction by considering a quadratic example and a cubic example.
There are 12 sets of cards, each set containing a polynomial function, its graph, the corresponding derivative function and the graph of the derivative function.
Possible matching activities
• use all four cards from each set (but perhaps not all the sets, depending on the time you have available). Shuffle each type of card, then ask students to match each function with its graph, the derivative function, and the graph of the derivative function.
• for a more difficult activity use just the graphs and match the graphs of polynomials and their derivatives, students will need to think carefully about the relationship between the features of the graph of a function and its derivative.
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