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Loch Ness

Draw graphs of the sine and modulus functions and explain the humps.

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The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

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Complex Countdown

Play a more cerebral countdown using complex numbers.


Age 16 to 18 Challenge Level:

Plot the graph of the function $y=f(x)$ where $f(x) = x(x+|x|)$. Find the first and second derivatives of the function. Show that the first derivative exists at $x=0$ but that the second derivative does not exist at $x = 0$.

This is a very simple question but it requires an understanding of how to handle functions that are defined differently on different parts of their domains.