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:

The function is undefined for $x=0$ but we need to find the limiting value as $x \to 0$ to answer the question.