Turning points

There are 12 NRICH Mathematical resources connected to Turning points
Curve fitter
problem
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Curve fitter

Age
14 to 18
Challenge level
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This problem challenges you to find cubic equations which satisfy different conditions.

Folium of Descartes
problem
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Folium of descartes

Age
16 to 18
Challenge level
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Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Witch of Agnesi
problem
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Witch of agnesi

Age
16 to 18
Challenge level
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Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
Discrete Trends
problem
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Discrete trends

Age
16 to 18
Challenge level
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Find the maximum value of n to the power 1/n and prove that it is a maximum.
Exponential Trend
problem
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Exponential trend

Age
16 to 18
Challenge level
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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.
Quick Route
problem
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Quick route

Age
16 to 18
Challenge level
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What is the quickest route across a ploughed field when your speed around the edge is greater?
Curve Hunter
problem

Curve hunter

Age
14 to 18
Challenge level
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This problem challenges you to sketch curves with different properties.

Patterns of inflection
problem

Patterns of inflection

Age
16 to 18
Challenge level
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Find the relationship between the locations of points of inflection, maxima and minima of functions.
Placeholder: several colourful numbers
problem

Bird-brained

Age
16 to 18
Challenge level
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How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
Least of All
problem

Least of all

Age
16 to 18
Challenge level
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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.