The formula for the radius of curvature at any point x for the curve y = f(x) is given by:Radius of curvatureRadius of curvature =[1+(dydx)2]3/2∣d2ydx2∣=∣∣∣dx2d2y∣∣∣[1+(dxdy)2]3/2ProofExample 1 Find the radius of curvature for the cubic ...
We can find the curvature by evaluating the first and second derivatives of the plane curve at the given value of the parameter. The curvature formula for the plane curve is κ=|y″(x)|[1+(y′(x))2]32. The radius of curvature of the plane curv...