Question

AS FAL: 1.0x1/5 + 1.0x1/5 + 1.0x1/5 + 1.0x1/5 + 1.0x1/5 = 20% + 20% + 20% + 20% + 20% 6 Original Response Unfiltered Response The temperature at any point (x, y, z) in space is T = x y z4. Find the highest temperature on the surface 3 x2 + 4 y2 + z2 = 6. Enter the exact value of your answer in the box below. 你的作答 無解答 正確答案 8/3*3^(1/2) 9:0/1.0 Warning: If your answer involves a square root, use either sqrt or power 1/2. Note: The highest temperature cannot be 0.

Answer 1

Given Т. Јz + and T is maximum. 4he Surface 818, 2) = 3х4 40°+22 4 го We have to find (2,4, 2 st solution points = ( 1 / 3 f2) Е ( + 2) Answers ч М «Т- V3 T-xg let f Ф f= (xj z+) - ( 31°+4)- 2-4 ) So, fх: ду21 - Ах го f;= х2+ - это f2= ҒА : -(3x+43% 22. 4) = 0 - Civ эзк?чј+2*4 =o 4 xj 23 2 А2 - о , we get X from (pxx 110 x — Ах3.5. о Д) x2 (10 x 45 we get VI со Хz". 16 x 7*z 3 E) * ( 25. 16 5*z3) =0 (11 x 2 1) х 48 - 32,5*+2 za o 2. (г. 1699) = 0 E)

UX4 & we get on x2 -24 122+ + 2x2²_o I- = 2x(2² 12 e²) = 0 Casey from Fild, let ato Xto =) z? 12x²=0 = 2 E o = 2² 1282 then from (ig, we get 8827492 + 122²=6 15x²7 4 7 2 = 6 1 =) vil If tt0 = from 2² = 1692 from (1) 3x²+ 4y2 +1692=6 =) 3x²+ 2042 = 6 SX (2 from, o x 1 I weget 49²-10042= 6-30 -969 2 - 24 =) y를 4 =) y = + 1 / Putting y = + 1/2 in ② we get 3r?+ 20.5 26 3x²+5 = 6 =) 3x²= 1 = ) =) x = 41 T3

Putting the values of no + 14/15 ,= 트 in the surface, we get 31 %) +41 + 2? 6=0 ) It i-6+ 2²0 =) 2= 4 2= 9 12:42 then solving corozim, weget Case-2 If x=0 which is not in the surface. g. 20, y=0,250 max T= ny24 80, pointo 4 15 Å x 1/2 x 16 = 2 -82) 73 maximum +2) -ve [2) -ve les ។ maximum ☆ - 2) V3 - So, we get its to it) & (ft. - 1 / 12) maximum Points where the value of T 4 V3 le max T = Ay

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