Instructions (1) Please write down your full name and SIM student number (2) Answer all questions (3) Calculators are not permitted (4) Submit your assignment in Canvas in pdf format (5) Due date: 17th October 2023, 10pm (6) The total marks is 20 marks 1. The function / and g are defined by /(z)=x+52+6 , g(x) =2-x'+r. Show that the curves y = /(x) and y = g(x) does not intersect and sketch the curves on a single diagram. For which values of c will the graph of f intersect the graph of the function h(x) = g(x) + c? For which particular value of c will there be precisely one point which they intersect? [10] 2. A firm produces a good from a raw material that costs 2 dollar per unit. Using 2r units of raw material, the firm can produce (2r)" units of its good, where a is a fixed number such that 0