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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.

Exponential Trend

Age 16 to 18 Challenge Level:

In order to differentiate this function and to find the turning points express it in the form $x^{1/x} = e^{1/x \log x}.$