You title this "curvature" but the problem is much simpler than calculating the cuvarture. r'(t)= < (12t^3)', (18t^2)', (9t^4)'>= <36t^2, 36t, 36t^3>. It's length is and the unit tangent vector, T(t) is <36t^2, 36t, 36t^3> divided by that: . T(1) is, of course, that evaluated at t= 1.