4. A toy car was released from the starting point of a layered race track toy set. The car then travelled around the circuit before crossing the nish-line. It took the car 3 seconds to travel from start to nish. The height of the car above the oor, in centimetres, at any given time is given by1 HE} : t4 5:3 + 5t2 +20 for D :2 t g 3 Where H is the height and t is tiJne in seconds. {a} What is the height of the race-track at the starting point and the nish-line? [2 marks] (1')) Find the following: (i) All the local maidma or minima [2 marks] (ii) Lnterva1{:s] where H is increasnigfdecreasing. [2 marks] (iii) Points of inection [2 marks] (iv) Intervals where H is concave downward Jlufwvard. [2 marks] ((2) Fully describe the path of the car in terms of its height and time using the information in (h). [2 marks]