Ask Copilot + 1 of 2 | | ED 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) Problem 2:Find the derivative & 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 1 i.e a,, and with respect to r2 i.e or, 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 , 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 Q Search 19 14 12 imort sc delete backspace R O P G H K ente M pause B N striFinal_Exam_Spring_23 - 2024 Sp: X Bb 162756328 X + -1-prod-fleet02-xythos.content.blackboardcdn.com/61aab133e7df2/162756328?X-Blackboard-$3-Bucket=learn-us-east-1-prod-fleet01 s password... B. Booking.com E OmarAbuzahriehRe... Al at | Ask Copilot + 2 of 2 | 2 | ID 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 - 12 -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 15x9 dx (ii) S(5x5 + 4x4 - 313 - 212 + r + 1) dx (iii) So }Vidx (iv) f? x(12 - 1) dx Problem 11:Let the Revenue function be TR = 2Q + 303 and Cost function be TC = Q3 +4Q2 + 4Q + 100. Derive the profit function and find the profit maximizing output (Q).(5 Points) Q Search M