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Calculus Analogies

Age 16 to 18
Challenge Level Yellow star
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It can be useful to hold your hands as if holding a wheel and imagine driving along a road!
 
Don't forget to focus your attention on the main concepts in the problem and don't get distracted by questions such as what if the road is not flat etc. This is a mathematical idealisation!
 
 

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Folium of Descartes

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Witch of Agnesi

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Discrete Trends

Find the maximum value of n to the power 1/n and prove that it is a maximum.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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