(a) Let y = f(x) be a smooth function in the x-y plane. Prove that the...

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(a) Let y = f(x) be a smooth function in the x-y plane. Prove that the curvature at each point on the curve is K(x) = |f" (x)| [1 + (f'(x))2]3/2 (b) Let r(t) = x(t)+(t)) be a smooth curve on the 2D plane. Prove that the curvature at each point on the curve is |x'y" - y'x" K = [(x')+(y')2]3/2 (a) Let y = f(x) be a smooth function in the x-y plane. Prove that the curvature at each point on the curve is K(x) = |f" (x)| [1 + (f'(x))2]3/2 (b) Let r(t) = x(t)+(t)) be a smooth curve on the 2D plane. Prove that the curvature at each point on the curve is |x'y" - y'x" K = [(x')+(y')2]3/2