Find a polynomial f(x) of lowest possible degree such that the curve y = f(x), 0 ≤ x ≤ 1, can be used to join the straight line segments y = 0, x ≤ 0, and y = 1, x ≥ 1, to form a curve along which a particle can travel at constant speed without experiencing discontinuous acceleration.
◦ f(x) = 4x2 - 7x3 + 4x4
◦ f(x) = 10x3 - 15x4 + 6x5
◦ f(x) = x5 - 3x6 + 2x7
◦ f(x) = 2x - 3x2 + 2x3
◦ f(x) = 18x4 - 30x5 + 13x6