1. Textbook (C&W) p227 Exercise 9.2/Q2 2. Find the stationary values of the following (check whether they are relative maxima or minima or inflection points), assuming the domain to be the interval [0, 50): (a) y= x3 - 3x + 5 (b) y = $x3 - x2 + x+ 10 (c) y= -x3 + 4.5x2 - 6x +6 2. Textbook (C&W) p233 Exercise 9.3/Q1, Q2 1. Find the second and third derivatives of the following functions: (a) ax + bx + ( (c) 3x 1 - x (x # 1 ) (b) 7x4 - 3x - 4 (d) 1 + x 1 - > ( x # 1) 2. Which of the following quadratic functions are strictly convex? (a) y = 9x2 - 4x +8 (c) u=9-2x2 (b) w= -3x2 + 39 (d) v= 8 - 5x + x2 3. Textbook (C&W) p241 Exercise 9.4/Q1, Q3, Q5 1. Find the relative maxima and minima of y by the second-derivative test: (a) y= -2x2 + 8x+ 25 (0) y= x3 - 3x2 + 5x + 3 (b) y = x3 + 6x2+ 9 (d) y= 2x ( x * 2 ) 3. A firm has the following total-cost and demand functions: ( = Q3 - 7Q2 +111Q+50 Q = 100 - P (a) Does the total-cost function satisfy the coefficient restrictions of (9.5)? (b) Write out the total-revenue function R in terms of Q. (c) Formulate the total-profit function . in terms of Q. (d) Find the profit-maximizing level of output Q". (e) What is the maximum profit? Note: the coefficient restrictions of (9.5) are a, c, d>0 b