C(x)=0.01x 3
−3x 2
+1108x+960 where x≥0 is the number of units produced and sold. (a) Find an expression for the profit function π(x) for x≥0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which π(x) is increasing and decreasing. (d) Determine the intervals over which π(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection. Question 6 (5 marks) Given the demand function aQ+bP−k=0, where a,b and k are positive constants, show that the price elasticity of demand is minus one when marginal revenue is zero.