SOLUTION: Find the radius of curvature of function f(x) = x + 1/x at point (1, 2)?

Question 1172369: Find the radius of curvature of function f(x) = x + 1/x at point (1, 2)?
Answer by ikleyn(52879) (Show Source): You can put this solution on YOUR website!
.


    The radius of curvature of a curve at a point M(x,y) is called the inverse of the curvature K of the curve at this point: 

                  R = 1/K. 


    Hence for plane curves given by the explicit equation y= f(x), the radius of curvature at a point M(x,y) 

    is given by the following expression: 


                  R = ((1+(y′(x))^2)^(3/2)) / |(y′′(x))|.

The rest is on you.

As the reference to the theory and examples, see the link

https://www.math24.net/curvature-radius/#:~:text=The%20radius%20of%20curvature%20of,%E2%80%B2%E2%80%B2(x)%7C.

https://www.math24.net/curvature-radius/#:~:text=The%20radius%20of%20curvature%20of,%E2%80%B2%E2%80%B2(x)%7C.

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