Question 5 (marks) a) Show all working. a) Find the derivatives of e2* sin(4x) and e2\" cos(4x). b) Using the results of part (i), show that 2f e** sin(4x) dx +4 | e cos(4x) dx = e** sin(4x) + Cy And 2f e~ cos(4x) dx +f e** sin(4x) dx = e** cos(4x) + C, where C; and C2 are arbitrary constants. C) Use the two equations from part (ii) to find | 10 e** sin(4x) dx (1+ 1+2= 4 marks) b) A company produces an item, where the production cost for them is $2 per item. They plan to sell each item for $x. Market analysis finds that in a week, \"2 items will be sold. What value of x will maximise their weekly profit? You should verify in some way that this value of x does indeed produce the maximum weekly profit. What is the maximum weekly profit? (4 marks)