Created by T Madas Question 228 (****) f ( x) = − 6x x2 , x ≠ a) Find the coordinates of the stationary point of f ( x ) and determine its nature b) Show clearly that f ( x ) has a point of inflection and determine its coordinates ( ) , − , Created by T Madas ( 2, −2 ) Created by T Madas Question 229 (****) non calculator The population, P in hundreds, of a herd of zebra t years after a certain instant is given by the formula P = 6t + 96 − 60 , t > t a) Find the number of zebra in the herd after years b) Find the time during which the herd’s population is increasing P = 1750 , t > Created by T Madas Created by T Madas Question 230 (****) x − 3) ( f ( x) = x3 , x ≠ a) Show clearly that f ′ ( x ) = A + Bx −2 + Cx −4 , where A , B and C are constants to be found b) Find the exact coordinates of the stationary points of f ( x ) and use f ′′ ( x ) to determine their nature c) Show that f ( x ) has two points of inflection and determine their coordinates f ′ ( x ) = + x −2 − 27 x −4 , ( ) ( ) ( )( 3,0 , max − 3,0 , 3, , −3, − 3 Created by T Madas )