Quiz 2 (1) - American University of Sharjah Department of...

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Unformatted text preview: American University of Sharjah Department of Math and Stat MTH203 * Calculus III — Quiz # 2 Instnuctor: A.__Sayfy r SummerEOOS ID#: Sec: Name: 7/, .‘ Q1. Find the local maxima, local minima, and saddle points of the function ,W a f(x,y)=4xy—x3-2y _ (xqu’lngx :chqu‘x—ZzJ “73 'Xilia‘j': if; C. J 1—H 4 2'7, 3" x x1 l‘.’/ “:1 Pig /C~jx (:14! Li 0 g 1 —-u—. if! ‘ ‘ a i /’/(l‘q|’§) 4" "’5' f 7'Tfi'fl/‘z‘fgl R (2 {5556/2 J); Q2. Use Lagrange multiplier to find the maximum and minimum values of .f‘(xa : 2x2); SUbjeCt tOJC2 + y2 : 4 . l” ‘1' = X-l‘t'SQ—L/ 7f 17/\ 9 €152 (L/Xjf2%2>:/\C?xl'gajf> 3:33; (9 m: '22vx audit—A) 9.x MM "' ‘ 2 fl ‘ . J/ 8/) ’X2 + j? : L, «:5 3:9 "‘ X :t: O ._ z _ l f; Q—37X —2-2~3~1 33x:7~j W/ ::-'\ ?j'l _\_ \j’L _: L/ 7:) VS i X : :j 9: J3 a r\ C 7 , 22 n a 3f , c/S 3 {Agni 3i )2 a? < max Wm,“ J‘— _ 7 — _, -.._ '2 # Lyme P7\l—é ' A12) - a??? e W\L\/‘ wt P, i Q3. Find the equation of the tangent plane to the surface 22 : x2 7 y2 at the ' t 5,—3,—4 . ‘ , ' . ‘ _, pom ( l i” f : x1, k5: # 3 L I Pub-1-1,”) _ i W, .. fig 3; . 4mm PM 6’ . » -> .- Jm R; F’ (1!; r"""'"' (I [(3, 6,331) a < pug—[3+3] gflf) :3. WK’5‘) *+ CWT 3) +5/%+c/J :3 I7! : <‘2x,—H,~??7 -: . a _ . -. ‘fo :c’w 0/ 3) X + '4: L' :1 v t J ’ ’ 3V3 ’ ? A '9 . ...
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