Turn over 15  Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 5 marks) 16   7. In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. x C O l R P(5, –13) y Figure 2 Figure 2 shows a sketch of part of the curve C with equation y = x3 – 10x2 + 27x – 23 The point P(5, –13) lies on C The line l is the tangent to C at P (a) Use differentiation to find the equation of l, giving your answer in the form y = mx + c where m and c are integers to be found. (4) (b) Hence verify that l meets C again on the y-axis. (1) The finite region R, shown shaded in Figure 2, is bounded by the curve C and the line l. (c) Use algebraic integration to find the exact area of R. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________