This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Name (printed): Question I
Find the ﬁrst partial derivatives of the functions f and 9 below: (a) 1%» y) = 1n(=v2y") (b) 90%) = w 005013?!) I?) 1% minim; mm mm mm: HM +41“, 5am MM WWW ELL—3. Eitﬂ...
3" X )‘hyqy‘ . x ’3 x .
m % _'ﬁ'(X‘*’M‘<z\) =~ ‘°‘5(*‘/)+ x3;L(mu./ﬂ (WM) '—
u. ’“Wﬂ  *‘rniwmx («9% mm L:  :3...
11 ‘ Mb‘wmm/W 7 *Xamb‘wﬂ (Mn MU Name (printed): Question 2
Evaluate the following double integrals, Where R is the triangle whose vertices are (0, 0), (a0), (5% ‘
(a) I :fchosydacdy
(b) [3, : fmeydwdy Name (printed): Question 3 (a) Determine the critical points of the function f(m, y) 2 £33 + :93 — 3m — 3y. (b) What information does the secondderivative test give about the nature of each critical point?
’H: 3 'BF : (a _.._i _. 3x 3 __. __ _
"Mk ) \Y 3x 31 (Hi3) (\},,.,ﬁ (1)”; (ﬁx).;\‘ 3.. 3 .
(‘3‘) Na lam2 midi: : 6* ha]: 1 (a? 31“.; 3x“ )3?“ J MM :0“ ”mi Di (m) w (“W °
w DU 5 H3 OJ DUJ~1\*°J D (HUQJ‘O D(—1~[)‘>Q a l J
ARM 39in) w: wmmJ—dw >0 (“Jq .40 Name (printed): Question 4
The food company Gnotrition produces 8ounce containers of its energy drink BARPH at its facility in Backwater, Colorado. The number of BARPH containers it can produce
per week with the expenditure of x units of labor and y units of capital is given by the production function
my) =5,000m1/3y2/3. Each unit of labor costs the company $ 2,000, and each unit of capital costs it $ 4,000. How
should Gnotrition choose a: and y so as to produce 10,000 containers of BARPH per week at minimum cost? \NQ MEL my Lﬁmmﬂa W QM taxi3W W “AA
23:5 M gchY} ., alonOX. + “i°°°‘/ )m M40? MM FIxJ‘f h) 1 11‘0qu \ thong.“ ‘r ‘\(]DJ000_ 5'0““ Kilafua) . T'owmmmmwaFn CD‘SYIM = 3” 4+4}? 4 i\(10 sx"‘*y"3) s J
M 14% 7% hm hm FM W4 M
M; 5.
‘— 3* \ “(3‘3’3 18;...
3X 3 X / ) \Y 4‘ jiiAxuqu/E
83.er 1E. '35;
3K N BY .. :3) ALT“ 33¢
S _:_‘
X . 13: XML/ “3) x _ _:_: qugw/H‘s ...
View
Full Document
 Spring '06
 Sarason

Click to edit the document details