# Resources tagged with: Turning points

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Broad Topics > Calculus > Turning points ### 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. ### Scientific Curves

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Make a catalogue of curves with various properties. ### Calculus Analogies

##### Age 16 to 18 Challenge Level:

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