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

Problem
Primary curriculum
Secondary curriculum
### Curve Fitter

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

Age 14 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Quick Route

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Discrete Trends

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Witch of Agnesi

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

Problem
Primary curriculum
Secondary curriculum
### Folium of Descartes

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

Problem
Primary curriculum
Secondary curriculum
### Bird-brained

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Patterns of Inflection

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Calculus Analogies

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curve Hunter

This problem challenges you to sketch curves with different properties.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Scientific Curves

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 16 to 18

Challenge Level