The motion of a football is described by the function (a t) (b+t) y (t) = (c t) where t is the time in seconds, y is the vertical height above the ground in metres and a, b and c are constants. a. Use the method described in Part 3 Example 5.8 to differentiate the function being careful to i. apply the methods of calculus to derive the formula you are using ii. describe your reasoning at every stage of the calculation (15 marks) b. Another function gives the following derivative dy dt = (0.45 t) (6+t) 230 - t Find the times at which the altitude is an extremum.