Please answer the following questions:

e3x-5 Q7. (a) A curve, C, has equation y = Show that C has exactly one stationary point. You must fully justify your answer. (6) (b) A curve has equation y = 6x2 + -2 and is sketched below for x > 0 Find the area of the region bounded by the curve, the x-axis, and the lines x = a and x = 2a, where a > 0, giving your answer in terms of a (4) (Total 10 marks) Q8. A curve has equation y = x - 2x2 + 9. The point P with coordinates (-1, 6) lies on the curve. (a) Find the equation of the tangent to the curve at the point P, giving your answer in the form y = mx + c. (5) (b) The point Q with coordinates (2, k) lies on the curve. i) Find the value of k. (ii) Verify that Q also lies on the tangent to the curve at the point P. (2) (c) The curve and the tangent to the curve at P are sketched below. (i) Find (x5 - 2x2 + 9) dx. (5) (ii) Hence find the area of the shaded region bounded by the curve and the tangent to the curve at P. (3) (Total 15 marks)