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  3. Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.
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Ian Fowler
Sep 18, 2020
  ·  Edited: Sep 20, 2020

Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.

As you might think, maximum curvature does occur at the stationary points, but it does not. You can find the exact values of x which are quite surprising and give you an insight as to how the curve behaves.

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Ian Fowler
  ·  Sep 19, 2020  ·  Edited: Sep 19, 2020

Bang on! It's so weird. The curve actually flattens out "slightly" between 1.0091 and 1. If asked this question I would have thought, off the top of my head, for sure the stationary point.


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whyareyoureadingmyusername
Sep 19, 2020


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whyareyoureadingmyusername
Sep 19, 2020

Or -1.00908

Ian Fowler
Sep 20, 2020  ·  Edited: Sep 20, 2020

And it all comes down to sqrt(86) instead of sqrt(81) and that, in turn, all comes down to the 1 in [1+(y")^2]. Amazing.


-1.00908 gives the minimum curvature if you leave out the absolute value.


It is also related to the fact that the curve is not symmetrical about it's stationary point. That's why you don't get a twin to the near left of 1.