(A) Create a polynomial function, p(), defined by the following features: the degree is 3; the coefficient of the leading term is 4; and the x-intercepts are at (2, 0), (-4, 0), and (6, 0). 12 marks]. (B) Create a polynomial function, q(@), defined by being a difference of cubes with a root at c = 2. [1 mark]. C) Let r(@) = P(I) q(I) . Calculate the following: (i) limr(x) [1 mark] (ii) limr(x) [3 marks] (izi) lim r(x) [2 marks] I-+100 (D) Calculate the following: (i) p' (1) [2 marks]. (zi) q'(1) [2 marks]. (iii) r (1) [3 marks]