There are 12 NRICH Mathematical resources connected to Turning points, you may find related items under Calculus.
Broad Topics > Calculus > Turning points
This problem challenges you to find cubic equations which satisfy different conditions.
What is the quickest route across a ploughed field when your speed around the edge is greater?
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.
Find the maximum value of n to the power 1/n and prove that it is a maximum.
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
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 calculus.
This problem challenges you to sketch curves with different properties.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.