Created by T Madas Question 116 (***+) The curve C has equation y = f ( x ) given by f ( x ) = ( x − 2) , x ∈ » a) Sketch the graph of f ( x ) b) Find an expression for f ′ ( x ) The point P ( 3, ) lies on C and the straight line l1 is the tangent to C at P c) Find an equation of l1 The straight line l2 is another tangent at a different point Q on C d) Given that l1 is parallel to l2 show that an equation of l2 is y = 6x − C1M , f ′ ( x ) = x − 24 x + 24 , y = x − 16 Created by T Madas Created by T Madas Question 117 (***+) r h A hollow container, made of thin sheet metal, is in the shape of a right circular cylinder, which is open at one of its circular ends The container has radius r cm, height h cm and a capacity of 1500 cm3 a) Show that the surface area, A cm , of the container is given by A = π r2 + 3000 r b) Determine the value of r for which A has a stationary value c) Show that the value of r found in part (b) gives the minimum value for A d) Calculate, to the nearest cm , the minimum surface area of the container SYN-A , r ≈ 7.816 , Amin ≈ 576 Created by T Madas Created by T Madas Question 118 (***+) y y= x2 x O The figure above shows part of the graph of the curve with equation y= x2 , x∈», x > Find the area bounded by the curve, the y axis, and the straight lines with equations y = and y = SYN-N , Created by T Madas