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