2: Differentiation Techniques (80 marks total) Your mark will be given as a percentage. [10 marks] 1. Find the derivative in each case. You need not simplify your answer. (5 marks) a. (5 marks) b. [10 marks] 2. a. (5 marks) b. 3. a. (5 marks) b. 4. . 3 1 5 2 . . Find an equation of the tangent line to the graph of: (5 marks) [10 marks] Find the derivative in each case. Simplify your answer. (5 marks) [10 marks] 3 . 1. 7 at 2 at 2. 7 For the function 24 11, (6 marks) a. Give all the points where the tangent line is horizontal. Note a point is given by two coordinates (_ , _). Give exact values. (4 marks) b. Give an equation of the tangent line at each of these points. Give exact values. [10 marks] 5. Find for . [10 marks] 6. Suppose that the number of items sold after months is modelled by 500 25 2 (3 marks) a. Find ' 6 and ' 12 . (3 marks) b. Find " 6 , " 12 . (4 marks) c. What do the answers in a. and b. tell you about [10 marks] 7. and Let (6 marks) a. Find (4 marks) b. Find 8 . [10 marks] 8. 1. Let ? . . A company determines the cost, in thousands of dollars for producing items is given by 75. 500 If it plans to boost production in months from now according to the function 30 7, how fast the costs will be rising 6 months from now