Given the curve x(u) = sin(u) + 2 cos(2u) and y(u) = cos(u) + 2 sin(2u). The parameter u does not represent time.

(a) Find the unit tangent vector T and the unit normal vector N when u = 0

(b) Sketch these vectors on the graph of the curve.

(c) Compute the curvature when u = 0.

(d) Suppose the curve represents a new slot car race-track, find the exact location where the normal acceleration of the car will be the largest if one keeps the car at constant speed.