Question

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Question 24 4 pts Find an equation of the tangent plane to the surface x2 + y2 += 704 at the point (8. - 8, 16). 16(x-3)-96y+8)+ 32-16) = 0 16(x-8)- 48(y+8)+ 32(2-16)=0 16x-8)+ 963 +8)+ 32(-16)0 16x-8)-96(+8)+ 163-16) = 0 16x-8)-96y+8)- 327-16) = 0

Answer 1

24) The equation of the tangent plane to the surface x+6y + z = 704 at the point (8, – 8, 16) x.8+ 6y(-8) + Z : 16=704 = 80 - 484 +1622704 since eanation of tangent plane of ant by car & run eavy +2wzed = 0 at the point Merg, , 211 is ann, & byy, ecazutuinen anleyeyide Wlze zihed=0 Now, 161x. 8) - 3.614+8) +32 (Z - 16)=0 = 8(n-8) - 48.(4+8)+16( 2-167-6 8x - 4y +16 2: 704=0 8n – 4y + 167= 704 Hence the tangent plane is 16 (R-8) - 96 Cage 8) & 32 CZ-16) = 0

ns) им, 8) = 5-ku tu? . . . ( т ) = 3м - 48 , 4ч (ил Ч) = - Cu +38 му (и , ) = си 6 че си, 4) = 6 В уса (ч) - с Now, &m ( 1 ) 8) - о >) - ) 3 м - 8 = 0 м2 2 2) - 6 и 240 9. 2 <a (и, ч) - о 4* - ) 9 4 - 44 = 4.28 [ 1 2) ( - ) - о -". - о, 2- then nao 4.2.2, then и е 2 so points are Co, o, 3), (2,2) - 5) One [we take any co-ordinate ob z since f is a feenction of x andy се о, о, ) 2 му (о,0 3) { ич (0, 0, 3) - eruu to, o, 3) - . o. o - (-)- 2 - 6 2 0 (0,0,37 is a saddle point.

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