Question

4. (a) A function f has first derivative f'(x) and second derivative 2 f" (x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. 3 marks] (ii) Use the f(x), and the First Derivative Test to classify each critical point.[3 marks] (iii) Use the second derivative to examine the concavity around critical points that are not stationary points (iv) Now consider the graphs of f(x) and f"(x) (You can use Desmos or any other graphing package here). Based on these and your investigation of critical points and concavity, sketch a possible graph of the function f(x) showing all critical values. [3 marks [3 marks] (b) An engineering firm has hired a Human Resources consultant to see how they can optimize the hourly productivity of its engineers. It is found through 'experiment' that in a large shared office the productive hours H that n number of engineers work each day, can be modelled by n2 +130 What is the optimal number of engineers the firm should allocate to one of its large offices to ensure maximum hourly productivity? 3 marks]

Answer 1

os tensling to+ 2Ct3)) ANE -3 ond -33 2o concave p

N13 3 -2 f,(X)20

3 21202 (n2+ 130 t1300