Hi,

I need to find the curvature k of y=sqrt(R^2 - x^2)

I know k = |f''| / (1 + f' ^2) ^1.5

But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/

Thanks in advance for the help.

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- Jan 4th 2013, 08:56 AMPStudent175Curvature of implicit equation
Hi,

I need to find the curvature k of y=sqrt(R^2 - x^2)

I know k = |f''| / (1 + f' ^2) ^1.5

But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/

Thanks in advance for the help. - Jan 4th 2013, 09:17 AMskeeterRe: Curvature of implicit equation
- Jan 4th 2013, 09:21 AMPStudent175Re: Curvature of implicit equation
Sorry how did you get y' = -x/y ?

I got y' = f' = -x(R^2 - x^2)^-0.5 from the chain rule - Jan 4th 2013, 09:30 AMskeeterRe: Curvature of implicit equation
implicit derivative ...

... note that is a constant

- Jan 4th 2013, 11:06 AMPStudent175Re: Curvature of implicit equation
Ok great thanks, could you also show how you got y'' = -R^2 / y^3 ?

- Jan 4th 2013, 11:18 AMskeeterRe: Curvature of implicit equation

quotient rule ...

multiply numerator and denominator by to clear the complex fraction ...