Question 1: Is the curve (locally) inside or outside the osculating circle at a local maximum of curvature?
Question 2:Is the curve (locally) inside or outside the osculating circle at a local minimum of curvature?
Question 3: Is the curve (locally) inside or outside the osculating circle at a point that is not a vertex?
Question 4:Explain the relation between the osculating circle and the tangent line.
Question 5:What happens to the osculating circle near inflection points (where the curve changes from right turning to left turning, or concave to convex)? Why?
Question 6: Sketch the osculating circle at the points indicated on the figures below.
1.Go to the concept page to read how to calculate curvature and radius of curvature.