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