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# Quiz 2 (2) - 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 lustiw§ayfx _ __ Summer 2.008 Name: Kt’j '9 And: 91/\ ID#: Sec: Q1. Find the local maxima, local minima, and saddle points of the function f(x,y):x3 *y‘l *nyJr 6 7— , l (x: :JfLﬁt—?le_z'xv:;2 . .1 W'Zixl ‘7) “pix :2 x(—2zxi;~a):2 :9 ":2 a xii-3“ ‘13:") -: l"— . L3 ,3 ~ “‘th PH ‘ Pt (0:9) I ()1 ("231 2?) Q16 :6-% 2‘ L. , 5X —Z l I, : -*?6X%) #L/ /-2 ,m '«lf’l lo ~2l ‘ 4/ ﬁst-PPM.» 13M?! ﬁddlf’fk ' " _—: 5—] J n p p, '3. libcz. {add/2ft. :\ 111’ I} ?, g f: WWva f(x,y):3x—y+6 subjecttox2 +y2 : AU 9 : X24: ji_l/ l7! : 173 e c" : J I 1 r K- .4 <§/-~I‘>:)\<?¥f2jf> \$4 xz'k‘j *é/w’ '3:2 /\’X F; x: 3/2» _l:2)\j -'-;‘\.s'_\/?)\ ‘11 ‘7'"? f '2 + . w W Z! : ‘3 X :g/VT“ ("5 C: Tp‘i‘é 9‘ x:-—S/JTQ .‘SZ’L/JT; C-:<£J+<§ mm \Jl Q3. Compute the directional derivative of f(x, y) 2 e49 at the point P(l,4) in the direction of V = —2i—j. In which direction f(x,y) has maximum change. Mm} : VI/ 1 u U: tr U “IL/j _ <--2 I ~1> :(FZ ._\B-<:,2: : > _ "‘5— x , -7 Z/ ) 6;"; 1/! 1 ,7 J? “(twat—‘5 Drthuw mm (/b/fr’ w f,} V/) ‘2 48% F, ..~—— 7 [DIN LIV—7. 1/" / ‘:<§r5,_i'3 "é P] (1/5!) ...
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Quiz 2 (2) - American University of Sharjah Department of...

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