Let p : R -> R, p(x) = -(x-1)' . a. Find the rule of p". b. How many points of intersection do the graphs of p and p- have? Let q : R - R,q(x) = -a(x -1)' , where a ER* . c. What are the possible number of solutions to q(x) = q"(x) ? d. One of the values of a such that q is tangential to q l is 27 Find the other value of a. e. Hence, find the values of a such that q(x) = q"(x) has three solutions. Now consider the family of curves t : R -> R,t(x) = -(x-1)(x2 + bx + c). f. Find the values of b in terms of c for which (x) = 0 has two unique real solutions