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Broad Topics >

Calculus > Turning points

##### Age 16 to 18 Challenge Level:

Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.

##### 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.

##### Age 16 to 18 Challenge Level:

Make a catalogue of curves with various properties.

##### Age 16 to 18 Challenge Level:

Can you fit a cubic equation to this graph?

##### Age 16 to 18 Challenge Level:

Can you sketch these difficult curves, which have uses in
mathematical modelling?

##### Age 16 to 18 Challenge Level:

Can you construct a cubic equation with a certain distance between
its turning points?

##### Age 16 to 18 Challenge Level:

Find the relationship between the locations of points of inflection, maxima and minima of functions.

##### Age 16 to 18 Challenge Level:

What is the quickest route across a ploughed field when your speed
around the edge is greater?

##### Age 16 to 18 Challenge Level:

Consider these analogies for helping to understand key concepts in
calculus.

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.