[8 marks] (4 marks) (4 marks) [7 marks] (2 marks) (3 marks) (2 marks) [10 marks] (6 marks) (2 marks) (2 marks) [10 marks] (6 marks) (2 marks) (2 marks) x23x4 5. LetF(x)={ 1+1 \"\"1 2 3:: 1 6. a. Sketch the graph of F. b. Is F continuous at x = -1? Explain why or why not using the denition of continuity. Suppose that number of residents, N (t) (in hundreds) in a small community after t years is given by N(t) = 0.11!2 + 2% + 5. a. What was the initial number of residents? b. Find the average rate of change of N over [1, 4]. c. Explain what the number in b. represents. Forf(x) = 5x2 + 3x 2 a. Find the simplied form of the difference quotient. b. Find f'(-1). c. Find an equation of the tangent line at x = -1. For f(x) = i 52x a. Find the simplied form of the difference quotient. b. Find f'(1). c. Find an equation of the tangent line at x = 1