>>444
合っています。
(a)
　F(U,V) = 2U + 3V + (2次以上の項),
　x = X-2,　y = Y+3,　z = Z-1　とおく。
　G(x,y,z) = G(X-2, Y+3, Z-1)
　　= F(X+2Y+3Z, (X-2)^3 + (Y+3)^2 - (Z-1)^2)
　　= F(X+2Y+3Z, 12X+6Y+2Z) + (2次以上の項)
　　= 2(X+2Y+3Z) + 3(12X+6Y+2Z) + (2nd.)
　　= 38X + 22Y + 12Z + (2nd.),
　G=0　⇒　Z = - (19/6)X - (11/6)Y + (2nd.),
　　　　　　z = - (11+19x+11y)/6 + (2nd.),
(b)
　D g(-2,3) = [ -19/6, -11/6 ]
　
(c)
　F(U,V) = 2U + 3V + (3/2)UU - UV + (5/2)VV + (3次以上の項),
　G(x,y,z) = G(X-2, Y+3, Z-1)
　　= F(X+2Y+3Z, (X-2)^3 + (Y+3)^2 - (Z-1)^2)
　　= F(X+2Y+3Z, X^3 -6XX +12X +YY +6Y -ZZ +2Z)
　　= {38X + 22Y + (663/2)XX + 336XY + 87YY}
　　　+ (12+91X+56Y)Z + (29/2)ZZ + (3次以上の項),

ここで G=0 とおくと
　Z = {-(12+91X+56Y) + √(144 -20X +68Y -10946XX -9296XY -1910YY)}/29 + (3rd)
　　= -(19/6)X -(11/6)Y -(13589/864)XX -(5767/432)XY -(2381/864)YY + (3rd)