? E?c′DHq′ x1′DKl=eE 1/ f ?￥v′??l′? (1) f(x;y) = (x?y +1)2; (2) f(x;y) = 3axy ?x3 ?y3(a > 0); (3) f(x;y) = xy q 1? x2a2 ? y2b2(a;b > 0); (4) f(x;y) = e2x(x+y2 +2y); (5) f(x;y) = sinx+cosy +cos(x?y)(0 ? x;y ? …2); (6) f(x;y) = (px2 +y2 ?1)2: 2X?y = ax2 + bx + c,4?¤BF ? (xi;yi);i=1,2,...,n ?¨Kl =eE p" ?a,b,c ? ?@￥ ?íBQZ?F. 3X? ü ? μn??￥USsY ^ A1(x1;y1);A2(x2;y2);:::;An(xn;yn) k pB? P ?D?n??  ?￥ üZ?Kl. 4 p/ f ?·?S?D =￥Kv′?Kl′ (1) f(x;y) = x2 ?y2;D = f(x;y)jx2 +y2 ? 4g; (2) f(x;y) = x2 ?xy +y2;D = f(x;y)jjxj+jyj? 1g; (3) f(x;y;z) = (ax+by +cz)e?(x2+y2+z2);a2 +b2 +c2 > 0;D = R3. 5 p￡ 1 (1) f(x;y) = Ax2 +2Bxy+Cy2 +2Dx+2Ey+FR2μKl′íKv ′ ?A > 0;B2 < AC; (2) f(x;y) = xy + 1x + 1y0 < x;y < +1μKl′íKv′. 6 !F(x;y;z)μ=¨ ?? ê? ?i O F(x0;y0;z0) = 0; Fx(x0;y0;z0) 6= 0: ) ??F(x;y;z) = 0 ??￥?f ?z = f(x;y)(x0;y0) ?￥′￥A1? sHq. p? x2 +y2 +z2 ?2x+2y ?4z ?10 = 0 ? ??￥z = f(x;y)￥′. 7 p/ ?f ?￥v′?l′ (1) (x+y)2 +(y +z)2 +(z +x)2 = 3 (2) z2 +xyz ?x2 ?xy2 ?9 = 0: 8X??é12p￥B M ???? p ?Kv￥ ???. 9μB vM ? zb =24cm1ü ?￥ H| S?B? ￠ P¤ ?Kv p ?H￥ `?fi?| ￥ zx(n/m). x2HHHqqq′′′DDD ? ? ?ììì μ μ μ ° ° °eee ? ? ?EEE 1. p/ f ? ?óHq/￥′ 2 (1) f = x+y ?x2 +y2 = 1 (2) f = x2 +y2 ?x+y ?1 = 0 (3) f = x?2y +2z ?x2 +y2 +z2 = 1 (4) f = 1x + 1y ?x+y = 2 (5) f = xyz ?x2 +y2 +z2 = 1x+y +z = 0 (6) f = ax2 +by2 +2hxy ?x2 +y2 = 1 (7) f = x2+y2+z2 ?(x2+y2+z2)2 = a2x2+b2y2+c2z2lx+my+nz = 0. 2 pf = xmynzpHqx + y + z = aa > 0m > 0n > 0p > 0x > 0;y > 0;z > 0-/￥Kv′. 3 pf ?z = 12(xn + yn)Hqx + y = l(l > 0;n ? 1)-/￥′i ￡ ü?a ? 0;b ? 0;n ? 1 H a+b 2 ?n ? a n +b 2 n : 4 pV ?B?78Kv￥éZ8. 5 p8B?7V ?Kl￥éZ8. 6 p?￥? M ???? ?Kl?. 7é1a￥M ′ M?  B ???Z? 6B ???b?   ￥éò1  H ? ì ???Z? ??? ?-?Kl. 8 pe??= ü ?a1x+b1y +c1z +d1 = 0a2x+b2y +c2z +d2 = 0￥ ?L￥K  ?b 9 p ?tLy = x2?°Lx?y = 1W￥K  ?. 10 px > 0;y > 0;z > 0 Hf ?f(x;y;z) = lnx + 2lny + 3lnz o 3 ?x2 +y2 +z2 = 6r2 ￥v′,￡ üa;b;c1? L ? H ab2c3 ? 108 a+b+c 6 ?6 : 11 !f ?f(x;y;u;v)F(x;y;u;v)G(x;y;u;v)=¨ V±? X1  ?0 @ Fx Fy Fu Fv Gx Gy Gu Gv 1 A ?12. 7 L(x;y;u;v) = f(x;y;u;v)+?1F(x;y;u;v)+?2G(x;y;u;v) ?P0(x0;y0;u0;v0) ^f ?L￥×??￡ ü?d2L(P0) > (<)0 HP0 ^f ?f? ?Hq F(x;y;u;v) = 0G(x;y;u;v) = 0 /￥Hql v′?. 4