2024 Spr X zm Passcode Required - Zoom X zm ECON 3410 Fundamental Metho X |+ d/execute/content/file?cmd=view&content_id=_84932633_1&course_id=_2327851_1 E OmarAbuzahriehRe.. A + of 2 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 41 Problem 2:Find the derivative a of each of the following functions (5 points) (a) z=2y3 + 3y2 Where y = 24 + 2 Problem 3:Find the partial derivative with respect to ri i.e ari oy and with respect to 12 i.e 312 ay for each of the following functions (10 points) (a) y=xi - $142 + 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 au, 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 M arch T+ 2 of 2 2 0 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 + 6x + 2 Problem 8:Find the first through the fourth derivatives of the following function (10 points) (a) y=x5 +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=x +6 Problem 10:Find the following.(16 Points) (i) f 15x9 dx (ii) (5x5 + 4x4 - 313 - 212 + r + 1) dr (ili) Jo }vidx (iv) ? x(12 - 1) dx Problem 11:Let the Revenue function be TR = 20 +303 and Cost function be TC = Q3 +4Q2 + 4Q + 100. Derive the profit function and find the profit maximizing output (Q).(5 Points) Jam arch