Consider a Continuous-Strategy game, in which two players each choose a positive number as follows: Player 1's strategy choice is the variable s1 = x > 0, and Player 2 selects s2 = w > 0. For now we only consider the payoff for P1, which is 1(x, w) = 40x xw x2 (a) plot 1(x, w) vs x for the P2 choices w = 4, 8, and 12, using Desmos or some other program, and include screenshots. What x value maximizes 1 for each of these w values? (b) using the first derivative, find the x which maximizes 1(x, 12), compare to (a) (c) using the same approach, find the x which maximizes 1(x, w), treating w as a constant. This maximizing x will be a function of w, the best response function BR1(w). By substituting w = 4, 8, and 12, you should obtain the locations of the maxima from part (a)