M (no subject) - nahiank3@gmail.cc x * Homework Help - Q&A from Onl x + V X C D A mail.google.com/mail/u/0/#inbox/FMfcgzGIIMQwdskKWzLVxnqJbzQhzfdD?projector=1&messagePartld=0.1 To fu : Apps H University of Houstrogress Report... & COMD writing assig.. $1 peer reviewed article.. O Life- Span Final Exa... @ HSES 260 exam 4 p... Q o Reading list = M Gmail ? Assignment 1 of 21,266 Compose 31 The Differentiation and Derivative Rules Inbox 16,661 The Linear Function Rule. Starred dy = 5 dy dy = 12 i) y = 5x +12 (Ans. dx ), ii) y = 5 -4" (Ans. dx 4 ), iii) y = 12x (Ans. dx inutes ago) Snoozed The Power Function Rule. Sent dy - =10x dy 4x3 dy = 12x3 Drafts 98 i) y =5x*(Ans. dx ), ii) y = x(Ans. dx ), iii) y = 3x*(Ans. dx COLLEGE IMPORTANT The Rules for Sums and Differences. More dy = 15x2 -14x+4 dz =-161 -2013 +1812 i) y = 5x' -7x2 + 4x +9 (Ans. dx "), ii) z=-81 -5t'+ 6t (Ans. dt + ap =-69+7 dy = 2815 -1845 iii) p = -3q' +7q -15 (Ans. dq ), iv) v = 4u' - 3u'(Ans. du The Product Rule. Meet dy = 75x4 -140x3 dy = 14x" +88x' +48x5 iy = 5x*(3x -7) (Ans. dx ), ii) y = (x* +8)(x* +11) (Ans. dx New meeting dy - 56x6 - 30x4 dy = 231x10 - 756.x8 iii) y = (4x2 - 3) (2x5) (Ans. dx Join a meeting ), iv) y = 7x (3x- -12) (Ans. dx dy = 54x8 + 75x* -64x3 dz =-38417 +7215 -120 v) y = (2x* + 5)(3x' -8) (Ans. dx ), vi) z = (3 -121')(5 + 4t") (Ans. dt Hangouts The Quotient Rule. Nahian + 10x - 6x dy =35x -18x5 3x8 -4x7 dy 15 ), ii) Y= x1 - 4x3 4x5 2x (Ans. dx 4x3 (Ans. dx 4 y = = z ak ), iii) 1-3x (Ans. You: helloooo 20x4 - 48x 15x2 dy 105x2 - 90x dx (1-3x)2 ), iv) 2x2 +7x-3 (Ans. dx (2x] + 7x-3)? ), Enable desktop notifications for Gm 6.x - 7 dy 26 V ) 8x -5 (Ans. dx (8x-5)' Type here to search O 12:50 PM 12/12/2021M (no subject) - nahiank3@gmail.cc x Homework Help - Q&A from Onl x + V X C D A mail.google.com/mail/u/0/#inbox/FMfcgzGIIMQwdskKWzLVxnqJbzQhzfdD?projector=1&messagePartld=0.1 To f Apps 4 University of Houst (1) Progress Report... COMD writing assig... $4 peer reviewed article.. O Life- Span Final Exa... @ HSES 260 exam 4 p... Q o Reading list = M Gmail The Chain Rule. y= U' 1 = 3x* +5 dy / dx dy = 72x (3x* + 5)5 y = (7x+9)2 dy / dx ? and ; find (Ans. dx ), ii) ; find (Ans. dy =98x +126 u =7x -4 dy / dx dy -= 140(7x -4)19 Compose dx ), iii) and ; find (Ans. dx of 21,266 31 y = (4x] -1)' dy / dx dy = 56x(4x2 -1)6 y=(x +3x-1)5 dy / dx iv) ; find (Ans. dx ). V ) find (Ans. Inbox 16,661 dx dy = (10x+15)(x2 +3x-1)* Starred inutes ago) Snoozed Sent Drafts 98 COLLEGE IMPORTANT More Higher-Order Derivatives. Meet For each of the following functions, find the second-derivative y = 7x' +5x3 +12 dy -=21x2 + 10x; New meeting i) d'Y = 42x +10 (Ans. dx dx 2 Join a meeting y = (2x+3)(8x2 -2) ii) dy = 48x2 + 48x -4; = 96x +48 (Ans. dx 5x y = - dy 5 d' y 30-90x Hangouts iii) 1-3x ( Ans. dx (1-3x) ' dx (1-3x)* ) Nahian + 7x2 dy _7x2 - 14x . d' y _ _ 14 iv) x-1 (Ans. dx (x-1) 'dx] (x-1)' ) z ak You: helloooo y = (8x -4) v ) dy = 24(8x - 4)?, dy (Ans. dx = 384(8x -4) Enable desktop notifications for Gm Unconstrained Optimization with One Choice Variable Type here to search O 12:50 PM 12/12/2021M (no subject) - nahiank3@gmail.cc x * Homework Help - Q&A from Onl x + V X C D A mail.google.com/mail/u/0/#inbox/FMfcgzGIIMQwdskKWzLVxnqJbzQhzfdD?projector=1&messagePartld=0.1 To fu : Apps University of Houstrogress Report... & COMD writing assig.. peer reviewed article.. O Life- Span Final Exa... @ HSES 260 exam 4 p... Q o Reading list = M Gmail Unconstrained Optimization with One Choice Variable ? 1. Maximize the following total profit function: II = -Q' +4802 -1800 -800 (Ans. Q = 30 provides a maximum and II = 10000) of 21,266 Compose 31 2. Minimize the following total cost function: TC 9' 8.50 600 27 Inbox 16,661 (Ans. Q = 12 provides a minimum and TC = 99) Starred Partial Derivatives inutes ago) Snoozed 3. Find the first-order partial derivatives for each of the following functions: Sent 1) = = 3x y' (Ans. =, = 6xy';z, =9xy") z = (6x+ 7y)/(5x+3y) -17y 17x Drafts 98 ii) (Ans. (5x + 3y)2zy (5x + 3y)= ) COLLEGE IMPORTANT 5x -35y 35x ii) 6x - 7y (Ans. (6x- 7y) 27zy (6x - 7y)? ) More iv) = = (x + y) (Ans. =x = 2(x+ y);z, = 2(x+y) ) v) = = (2x-5y) (Ans. Zx = 6(2x -5y)';z, =-15(2x -5y)?) 4. Find the second-order direct partial derivatives (xx> >y)and the cross partial derivatives Meet (xy , yx) for each of the following functions: i) = = 3xy (Ans. Z, = 3y ;2xx = 0;2, = 6y;2, = 6xy; 2,, = 6x; 2,x = 6y) New meeting ii) = = x' + 2xy + y' (Ans. => = 2x+ 2y;2> = 10;zyg =12) of 21,266 v) z=8x'y-1 1xy' 2, =16xy -lly ;2= = 16y;2 =16x-33y2; Inbox 16,661 (Ans. Z, = 8x - 33xy' ; 2, = -66xy; 2, = 16x -33y?) Starred inutes ago) Snoozed 5. Given the function = =3x+ 2y' -xy -4x -7y +12 (i) find the extreme values (Ans. x = 1; y = 2, (ii) determine whether the function is at a maximum or minimum (Ans. Minimum: Sent Exx (= 6),Z,y (=4) 0), and (iii) evaluate it at the critical values (Ans. 3). Drafts 98 COLLEGE IMPORTANT 6. Given the function = =9x -3x- + 6xy -8y' +12y(i) find the extreme values (Ans. x = 3.6; y = 2.1, (ii) determine whether the function is at a maximum or minimum (Ans. Maximum: More Eux (=-6),z,(=-16) 0), and (iii) evaluate it at the critical values (Ans. 28.8). + Constrained Optimization with One Choice Variable 7. What combination of goods x and y should a firm produce to minimize costs when the joint cost Meet function is c= 6x- + 10y" - xy +30 and the firm has a production quota of *+ y = 34? and (ii) New meeting Use bordered Hessian "| to test the second-order condition. Join a meeting (Ans. () *= 21,y =15; (ii) H| = -34 0, the bordered Hessian is negative definite and profits are maximized. Enable desktop notifications for Gm Type here to search O 2 71OF ~ ( 40 41 ) ) 12:50 PM 12/12/2021