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February 27th, 2015, 02:31 PM   #1
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How to calculate a curvature of the cubic function.

Hi,
I need some help. I have a cubic function: f(x)=ax^3+bx^2+cx+d and I need to say (to prove) which formula is better to use to calculate a curvature: k=1/R or k=f''(x)/(1+(f'(x)^2)^3/2. The answer have to be proved. Maybe there is no difference and they both give me the same result, but I have to prove it.

(Here is the link, where are the both formulas: Curvature - Wikipedia, the free encyclopedia)
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February 28th, 2015, 12:38 AM   #2
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There isn't an easy way to calculate R, so use the second formula. The numerator should be |f''(x)|.
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March 2nd, 2015, 11:31 AM   #3
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But I have to explain, why the second formula it's better than first one. Maybe it's more accurate or something else. I got the task, that, based on the theory I have to explain and prove which formula it's better to use.
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