Question

The radius of curvature for the curve y=x_x/2 at (1,1/2)

Answer 1

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=1K. 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]32|y′′(x)|.