Turn over 15 Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 7 marks) 16 7. y P O x Figure 1 Figure 1 shows a sketch of the curve C with equation y = 4 2 2x x x + − 4 ln x        x > 0 (a) Show that d d y x = 12 16 4 2x x x x x + − (4) The point P, shown in Figure 1, is the minimum turning point on C. (b) Show that the x coordinate of P is a solution of x = 4 3 12 2 3 −     x (3) (c) Use the iteration formula xn+1 = 4 3 12 2 3 −       xn with x1 = 2 to find (i) the value of x2 to 5 decimal places, (ii) the x coordinate of P to 5 decimal places. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________