3. The derivative of a function f(x) is given by, f'(x) = 72/3(12 - 2) 1/3 ' Also, f(x) is defined at all its critical points. (i) Using f'(x), find all critical values of f(x). [3 marks] (ii) Use the First derivative test to determine the intervals on which f(x) is increasing or decreasing and hence determine which critical values will give a relative maximum or relative minimum - if any. [6 marks] 32 (iii) Use f"(x) = -- x5/3(12 - x)4/3 to examine the behaviour of f(a) over a small interval either side of x = 0. How would you classify the point (0, f(0)), and explain why the gradient does or does not exist at (0, f(0))? [7 marks]