Created by T Madas Question 291 (*****) R H R The figure above shows a hollow container consisting of a right circular cylinder of radius R and of height H joined to a hemisphere of radius R The cylinder is open on one of the circular ends and the hemisphere is also open on its circular base The cylinder is joined to the hemisphere at their open ends so that the resulting object is completely sealed Given that volume of the container is V , show the surface area of the container is minimised when R = H , and hence show further that this minimum surface area is 45π V SYN-W , proof Created by T Madas Created by T Madas Question 292 (*****) A curve C has equation y= 2x + , x∈» , x > 2x −1 Find the coordinates of the stationary point of C , further determining the nature of this point You may not use the product rule, the quotient rule or logarithmic differentiation in this question ( ) SYN-U , max , Created by T Madas Created by T Madas Question 293 (*****) The point P , whose y coordinate is , lies on the curve with equation y= k + 8x x , x∈» , x > , 12 x where k is a non zero constant The tangent to the curve at P is parallel to the straight line with equation x + y = 17 Determine the value of k SYN-T , k = Created by T Madas