Resources tagged with: Turning points

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There are 12 results

Broad Topics > Calculus > Turning points

Exponential Trend

Age 16 to 18
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.

Scientific Curves

Age 16 to 18
Challenge Level

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

Witch of Agnesi

Age 16 to 18
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.

Folium of Descartes

Age 16 to 18
Challenge Level

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

Curve Fitter

Age 14 to 18
Challenge Level

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

Curve Hunter

Age 14 to 18
Challenge Level

This problem challenges you to sketch curves with different properties.

Bird-brained

Age 16 to 18
Challenge Level

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

Least of All

Age 16 to 18
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.

Discrete Trends

Age 16 to 18
Challenge Level

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

Quick Route

Age 16 to 18
Challenge Level

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

Patterns of Inflection

Age 16 to 18
Challenge Level

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

Calculus Analogies

Age 16 to 18
Challenge Level

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