problem

Favourite

### Curve fitter

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

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Curve fitter

Favourite

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

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Folium of Descartes

Favourite

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

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Witch of Agnesi

Favourite

Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.

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Discrete Trends

Favourite

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

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Exponential Trend

Favourite

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.

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Quick Route

Favourite

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

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Patterns of inflection

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

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Bird-Brained

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

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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.