Question

Please answer number 6, and show and expkain your steps thank you

6. Find the absolute maximum and minimum values of fon D, where f(x,y)= x’ – 2xy +2y and D={(x,y)|05x53,0 sys2}. 7. Evaluate the integral [[ V«?+1d4, where D is the region bounded by the lines D y=0 and x =1, and the curve x= vy. You must evaluate this integral by hand and show all the steps that lead to your answer. Give the exact answer.

Answer 1

flming) - -7720 D = {(migogns 3 32 fx (mig) 23 critical -o - 2n+2 points. Sto =) n=1 is the crittal point. g) (1,1) is critical point. 2341 22f S ana 19 2 . r = 2 2 t=0 s = -2 st-s²= 240 - (~292 on (-2)2 rt-s2 < 0 of (mig) is neithe maximen nos minum at (1,1) 12 – 2x1x1 +27 1 = neither mininga nor maxina f(0,2) = 9 f (310) = 9 f (1,2) f(3,2) 1 10,0) 0 maximem aut (3,0) of (3,0) = 9 man at (0,0) 10,6)

13,2) (2) (11) (0,01 13,0) Critreal lies Inside the point the region Y ct u= To of (3,0) = n² incucering n23 3 9 maxina 3. 2. 1 ។ 1 0 minima. 12 = f( Big 92 -77393 4sy =ag bytay -g-47 03752 decuasting وا 0 = ? f(^,2) 2 m2 + 2x2 unty for coitical < value. parabolic functia au, 2 m ។ na 4 f(2,29 = 2² - 2x2x2 + 2x2 = 8- 8 = 0

nal 030 g 2 n=59 m3+1 dA S15 an 12 १२ J Be an dag dn Susredy 0 0 n2u34 an S n341 y Jan dua 0 D

3 श । १२ J 341 an मा = 3n2 dna at de V daa 21 3 * Stratat 31 प -- -)-"-21-2 52 2 t dt 2 12 3 3 3 3/2 2 2 D -- (15)-11 9