1 . (a) Given y = xemx. (i) Find the value of m which satisfy dy - = 24eat x =2. dx [4 marks] (ii) Hence, determine x- d'y dy _sy dx 2 -(5x+1) dx [5 marks] (b) Sketch the graph of a function that satisfies all the given conditions: f' (0) = f'(2) =f'(4) =0, f' (x) >0 if x4, f"(x) >0 if 1 3. [6 marks] 2. For the function f (x) = x +3x3 -9x +6, find (a) the open interval on which f (x) is increasing or decreasing. [7 marks] (b) the local extrema. [4 marks] (c) the value of the absolute extrema on [-4,4]. [4 marks]