Consider a plane curve with a regular twice continuously differentiable parametrization r(t) = (x(t), y(t)). Then at the point r(t), the curvature of the curve is - x' (t)y"(t) — x" (t)y' (t) ||r' (t)||³ and the corresponding radius of curvature is R = 1/| K | K = a) What kind of expression is obtained for the curvature of the graph of the function y = f(x) at its f'(x) = 07 0? critical point, where f"(x) b) b) What about at the inflection point of the graph, where = 0? c) Determine the radius of curvature of the parabola y = x² at the point (0, 0).

Q: Use the formula (x) K(X) = = y = 3x4 = |f"(x)| [1 + (F'(x))²] ³ 3/2 to find the curvature.

A: y=3x4

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Q: Use the formula x(x) = = K(x) = y = 3x4 |f"(x)| [1 + (²²(x))²] ¹ to find the curvature.

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