Created by T Madas Question 279 (*****) y O C A D B x The figure above shows a cubic curve whose coefficient of x3 is The curve crosses the x axis at A ( a,0 ) and touches the x axis at B ( b,0 ) , where a and b are positive constants The point C is a local maximum of the curve The point D lies on the x axis so that CD is parallel to the y axis Show, with a detailed method, that AB = AD SYN-O , proof Created by T Madas Created by T Madas Question 280 (*****) A solid right circular cylinder of fixed volume has radius r and height h Show clearly that when the surface area of the cylinder is minimum h : r = :1 proof Created by T Madas Created by T Madas Question 281 (*****) y y = A − x 2a x O y = B − x 2b The figure above shows the curves with equations y = A − x a and y = B − x 2b , x ≥ , where A and B are positive constants with A > B , and a and b are positive integers with a + b = Both curves meet the x axis at the point ( 2,0 ) Find the exact value of x for which both curves have the same gradient − 14 SP-F , x = Created by T Madas