This question is about the function g(x) = exp( 3 x1/3 - 1/2 x2). (a) Show that g'(x) = (x -2/3 - x ) exp( 3 x1/3 - 1/2 x2 ), explaining any rules you use and showing all of your calculations. (b) Find the critical point(s) of this g(x), justifying why you have necessarily found them all. (c) Use the first derivative test to determine whether each of the critical point(s) is a local minimum, local maximum, or neither. (d) Find the absolute maximum and absolute minimum of the function g(x) on the closed interval from 0 to 3.3, showing all of your reasoning and calculations. Write the absolute minimum in the box below, correct to 3 decimal places