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How do you find the curvature of a curve of $y=2x-x^2$ at the point where $x=1$ ?

If someone could provide me a little step by step, that would be great!

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One can always start with the definitions. How do you define the curvature of $y$ at a point? –  Pedro Tamaroff Aug 17 '13 at 3:10

1 Answer 1

up vote 1 down vote accepted

$$k(x)=\frac{y''}{(1+y'^2)^{3/2}}$$

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does that equation always hold true –  user90705 Aug 17 '13 at 3:19
    
@user90705 Yes, as long as the function is continuous. –  Ataraxia Aug 17 '13 at 3:39
    
and should it be the absolute value of the 2nd derivative of y –  user90705 Aug 17 '13 at 3:45
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@user90705: That depends upon whether you want the signed or unsigned curvature. –  Anthony Carapetis Aug 17 '13 at 5:28

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