Two Special Cubes is a RISP activity designed to introduce the idea of implicit differentiation. Students are presented with two cubes of length x and y and are told that volume, the surface area and the edge length form an arithmetic progression. Students are asked to find the maximum value for y and hence the corresponding value for x.
Never Positive asks students to think of two functions that are never positive. Students explore the nature of the resulting functions when the originals are added, subtracted, multiplied. This leads to students being asked to verify their results by differentiation.
Advanced Arithmagons has a variety of suggestions for using arithmagons to practice algebraic manipulation, product rule and quotient rule and the idea could be extended to other topics.
Differentiation Rules OK requires students to form an equation from the given cards, differentiate the results and find as many different values for y’(1) as possible.
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Resource by: RISPs