??? - 2013 JUNE Q9
9. Fig. 7 shows a sketch of the curve y= x3 - 3x2 - 22x+24 and the line y=6x+24
i) Differentiate y= x3 - 3x2 - 22x+24 and hence find the x-coordinates of the turning points of the
curve. Give your answers to 2 decimal places. [4]
(ii) You are given that the line and the curve intersect when x = 0 and when x = -4. Find algebraically the x-coordinate of the other point of intersection. [3]
(iii) Use calculus to find the area of the region bounded by the curve and the line y = 6x + 24 for -4≤ x ≤ 0 , shown shaded on Fig. 9. [4]
(ii) You are given that the line and the curve intersect when x = 0 and when x = -4. Find algebraically the x-coordinate of the other point of intersection. [3]
(iii) Use calculus to find the area of the region bounded by the curve and the line y = 6x + 24 for -4≤ x ≤ 0 , shown shaded on Fig. 9. [4]