MT1 2010 Solutions

MT1 2010 Solutions - Name(printed Question I Find the...

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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 second-derivative 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 lam-2 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 (“J-q .40 Name (printed): Question 4 The food company Gnotrition produces 8-ounce 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 taxi-3W 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‘ jiiAxu-qu/E 83.er 1E. '35; 3K N BY .. :3) ALT“ 33¢ S _:_‘ X .- 13: XML/ “3) x _ _:_: qugw/H‘s ...
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