There are **12** NRICH Mathematical resources connected to **Turning points**, you may find related items under Calculus.

Challenge Level

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

Challenge Level

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.

Challenge Level

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

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.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

This problem challenges you to sketch curves with different properties.

Challenge Level

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

Challenge Level

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

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.