Q2 (35 pts) Derivative and Optimization. Showing your analytical work clearly in a step by step manner is a must. Otherwise points will be deducted. You can use Excel or any other graphing tool. A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 a) 5 pts Find the marginal cost analytically, and draw its graph b) 5 pts Find the marginal revenue analytically, and draw its graph c) 5 pts Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. d) 10 pts Write the profit function and draw its graph e) 10 pts is the profit function concave up or concave down