Final_Exam_Spring_23 - 2024 Spr X zm Passcode Required - Zoom x zm ECON 3410 Fundamental Metho X + y.edu/webapps/blackboard/execute/content/file?cmd=view&content_id=_84932633_1&course_id=_2327851_1 password... B. Booking.com OmarAbuzahriehRe... V Draw Q T A + 2 1 1 of2 | 2 1 D ECO 3410 Fundamental Methods of Mathematical Economics Spring 2023 Final Exam Due:-05/17/2023 Problem 1:Find the derivative of each of the following functions (16 points) (a) y=10x-3 (b) (3x4 - 2) (c) (7x+9)(8x2 - 7x) (d) 2 Problem 2:Find the derivative d of each of the following functions (5 points) (a) z=2y3 + 3y? Where y = x1 + 2 Problem 3:Find the partial derivative with respect to T1 i.e ,, and with respect to 12 i.e or, for each of the following functions (10 points) (a) y=xi - T142 + 12 Problem 4:Find the total differential , for each of the following functions (5 points) (a) z=x2 + 2y+ 4y212 Problem 5:Find the total derivative du, for each of the following functions (8 points) (a) y=10x-w Where r = 9w + w3 +4 Problem 6:Find the critical value of the following functions (Check whether they are relative max- ima or Minima or neither of them) by Neighbourhood method (First derivative). (10 points) (a) y=x2 - 361 + 8 6:08 PM Q Search M 5/8/2024 end 10 144 "prt sc delete home backspace 6 T O P home G H J Kckboard/execute/content/file?cmd=view&content_id=_84932633_1&course_id=_2327851_1 AD king.com OmarAbuzahriehRe... + 2 of 2 Problem 7:Find the relative extreme of the following functions (Check whether they are relative maxima or Minima or neither of them) by second order derivative method. (10 points) (a) y=x3 - 4.5x2 + 6r + 2 Problem 8:Find the first through the fourth derivatives of the following function (10 points) (a) y=x + x4 - x2 - 3x + 1 (b) y=9x5 + 8x -10 Problem 9:Find the critical values of the following functions and use Nth-Derivative test whether they are represent relative maxima, relative minima or nothing. (5 points) (a) y=x4 + 6 Problem 10:Find the following.(16 Points) (i) f 15x3 dr (ii) S(5x5 + 4x4 - 323 - 2x2 + r + 1) dr (iii) Jo }vadx (iv) fix(x2 - 1) dx Problem 11:Let the Revenue function be TR = 2Q + 3Q3 and Cost function be TC = Q3 +4Q2 + 4Q + 100. Derive the profit function and find the profit maximizing output (Q).(5 Points) Q Search $12 mort sc delete hom 144 & backspace 6