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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Sep 18
· Edited: Sep 20Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.
Find the values of x where the curve f(x) = x^3 - 3x achieves maximum curvature.
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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.
Or -1.00908
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.