Other tags that relate to Polar Flower
Graph sketching. Mathematical reasoning & proof. Biology. Graphing software and graphical calculators. Symmetry. Creating and manipulating expressions and formulae. Polar coordinates. Trigonometric identities. Expanding and factorising quadratics. Quadratic equations.There are 11 results
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.
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.
Patterns of Inflection
Age 16 to 18 Challenge Level:
Find the relationship between the locations of points of inflection, maxima and minima of functions.
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.
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.
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?
Scientific Curves
Age 16 to 18 Challenge Level:
Can you sketch these difficult curves, which have uses in mathematical modelling?
Calculus Analogies
Age 16 to 18 Challenge Level:
Consider these analogies for helping to understand key concepts in calculus.
NRICH is part of the family of activities in the Millennium Mathematics Project.