
Turning points


problem
Curve fitter
This problem challenges you to find cubic equations which satisfy different conditions.

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

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

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

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

problem
Least of all
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.

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

problem
Exponential trend
Find all the turning points of y=x^{1/x} for x>0 and decide
whether each is a maximum or minimum. Give a sketch of the graph.

problem
Discrete trends
Find the maximum value of n to the power 1/n and prove that it is a
maximum.