Question

2. Consider the function f(r) = (x2 - 4x +5) e-r, for r > 0. (a) What is f(0)? (1 mark) (b) What is lim + S (2)? (No calculations necessary) (1 mark) (c) Calculate the first and second derivatives: f'(o) and l" ). (4 marks) (d) Using your previous answers, sketch f(x) for 2 > 0. Label the y-intercept, and any critical or inflection points. (hint: remember to factor your answers for f'(x) and F"(x), this will help you to draw sign diagrams). (4 marks)