Created by T Madas Question 197 (****) The cubic curve with equation y = ax3 + bx + cx + d , where a , b , c are non zero constants and d is a constant, has one local maximum and one local minimum Show clearly that b > 3ac SYN-B , proof Created by T Madas Created by T Madas Question 198 (****) y L1 y = x2 − x + Q P R O x L2 The figure above shows the curve C with equation y = x2 − x + C crosses the y axis at the point P The normal to C at P is the straight line L1 a) Find an equation of L1 L1 meets the curve again at the point Q b) Determine the coordinates of Q The tangent to C at Q is the straight line L2 L2 meets the y axis at the point R c) Show that the area of the triangle PQR is one square unit C1B , y = x + , Q (1, ) Created by T Madas Created by T Madas Question 199 (****) The figure below shows the design of a hazard warning logo which consists of three identical sectors of radius r cm, joined together at the centre Each sector subtends an angle θ radians at the centre and the sectors are equally spaced so that the logo has rotational symmetry of order θ r The area of the logo is 75 cm a) Show that the perimeter P cm of the logo is given by P = 6r + 150 r b) Determine by differentiation the value of r for which P is stationary c) Show that the value of r found in part (b) gives the minimum value for P d) Find the minimum perimeter of the feeder r = , Pmin = 60 Created by T Madas