Created by T Madas Question 203 (****) y y = x2 − x + P L1 R Q L2 O x The figure above shows the graph of the curve C with equation y = x2 − x + The point P is the point where C meets the y axis so that the straight line L1 is the normal to C at P a) Find an equation for L1 ( ) The point Q 3, lies on C and the straight line L2 is the normal to C at Q The finite region R , shown shaded in the figure above, is bounded by L1 , L2 and C b) Find the area of R SYN-J , y = x + , 15 Created by T Madas Created by T Madas Question 204 (****) 6x L 8x The figure above shows a triangular prism with a volume of 960 cm3 The triangular faces of the prism are right angled with a base x cm and a height of x cm The length of the prism is L cm a) Show that the surface area of the prism, A cm , is given by A = 48 x + 960 x b) Determine an exact value of x for which A is stationary and show that this value of x minimizes A c) Show further that the minimum surface area of the prism is 144 100 cm SYN-Z , x = 10 ≈ 2.15 Created by T Madas Created by T Madas Question 205 (****) non calculator y= Show that the value of d2y dx 2 − 3 , x ∈ » , x > xx where x = , is 16 proof Created by T Madas