**??? - 2013 JUNE Q9**

9. Fig. 7 shows a sketch of the curve

*y*=*x*^{3}-*3x*^{2}-*22x*+24 and the line*y*=6*x*+24i) Differentiate

(ii) You are given that the line and the curve intersect when

(iii) Use calculus to find the area of the region bounded by the curve and the line

*y*=*x*^{3}- 3*x*^{2}- 22*x*+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*= 6*x*+ 24 for -4≤*x*≤ 0 , shown shaded on Fig. 9. [4]