Investigate the family of graphs given by the equation x^3+y^3=3axy
for different values of the constant a.
Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.
Make a catalogue of curves with various properties.
Can you sketch these difficult curves, which have uses in
Can you fit a cubic equation to this graph?
Find the relationship between the locations of points of inflection, maxima and minima of functions.
Consider these analogies for helping to understand key concepts in
Can you construct a cubic equation with a certain distance between
its turning points?
What is the quickest route across a ploughed field when your speed
around the edge is greater?
A point moves on a line segment. A function depends on the position
of the point. Where do you expect the point to be for a minimum of
this function to occur.
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.