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quiz6_sol

# quiz6_sol - i i i i i l i E i i i MATH 174 1 Let z = f(x,y...

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Unformatted text preview: i i i i i l i E i i i MATH 174 1. Let z = f(x,y) = Vmﬁi—y, Quiz 6 Tuesday Mar 8 Section: PID: (2pts) (a) ﬁnd an equation for the tangent plane of z = f ( ,y)at (4, 9) (2pts) (b) use the linearization L(:c, y) of the function f(as, y) at (4, 9) to approximate f ( 8.) ZX . my a S“? M FW~‘§»%‘3' flag) 1?} L) FX’IfM: am @zh: w 1017,.) MW?” if 1. m: J, (9 Lung): fatal? 1 ‘fx‘tvm {MPH “JCMWDW’W : 5+ 0%DH”+ ”(VJ/l) {(1% g; 1,1118) 4 (xi #:4112974 751(57):?“ if“ 75 ‘3 3‘. (3pts) 2. Find all the critical points of the function f (as, y) : 6:132 — 2x3 + 3312 + 61:3; and identify them as the local maxima, local maxima or saddle points. M: fxﬁ [ZX-réXL—fby t/D it,» IZX~6Xl-[7X:q> ":r> X130 W X21, 3L3: ()‘Yrtb‘x :0 "3) X: ”‘7 y; ,X :2» ya) M‘s/Vs-) Onii‘évl ,0th m (U o“) M U r!) gay/<6 a: 2+yz< 5’") O ”((7/9)“ “PW/4'} \$54 Oah‘a/l Pf er : 2X "HL'DO a» X~y .jrx’cwy-so owlml [71L (Z.a7 MW (270) V3 U“? (in 125ny [12" MC 21+ 01 7% 7(3 A?!) IMO Ont/1‘60] Pt Iggl‘éiﬂ. 1. ‘> I w Ute/Z, x1471» chxfyy few/K 1 Ply (V51 atcw) jam-F” {WI (/2 avg é<0 you SFMlzfzaL (3pts) 3. Find absolute maximum and minimum values 0% f (m y)— — \$102+ 2y2 — 4:10 on the 3) 75% 7M 'JC’MX: 5 0: 3’ fag-:3 05661 D) 3 (a BMW 013‘ x1472 >19 yzsw jalxﬂv: 0(14l(1#3<l)—~Q><r, r-XLrU/X-Fl :3”) g/(SC): "“ZX’q/co 2‘) X: “2/ XML,” ) “:;> 91x) AM; no 001451] Pt m Xl+>/1;, (36m: “'X’ZerX +2 \l r‘ (X‘I-Z/jg—{lé k 014% MW XEWZ~ ...
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