Differentiation of parametric and implicit functions

There are 3 NRICH Mathematical resources connected to Differentiation of parametric and implicit functions

problem

Favourite

Folium of Descartes

Age

16 to 18

Challenge level

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

problem

Favourite

Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

problem

Implicitly

Age

16 to 18

Challenge level

Can you find the maximum value of the curve defined by this expression?