... (0, 0) (1, 1) D 1 =6> 0,D2=27> 0 Hf (1, 1) > 0 f (1, 1) 1 0(φ 1 (t), ··· ,φm(t))dt =( 1 0φ 1 , ··· , 1 0φm)f : U → RmU Df(x)=0, ∀x ∈ Uf ≡f : U → RnU ⊂ RnC 1 KU ... ··· , ( 1) nDn> 0.f(x, y)=x 3 + y 3 − 3xyf∂f∂x=3x2− 3y =0,∂f∂y=3y2− 3x =0.(0, 0) (1, 1) fHf =∂2f∂x2∂2f∂x∂y∂2f∂y∂x∂2f∂y2=6x 3 36 y(0, ... b) θ ∈ (0, 1) g(x+h)=g(x)+ 1 1!g(x)h+ 1 2!g(x)h2+···+ 1 (k 1) !g(k 1) (x)hk 1 + 1 k!gk(x+θh)hk.f : Rn→ Rg(t)=f (x + th),t∈ [0, 1] .∇ =(D 1 , ··· ,Dn)=(∂∂x 1 , ··· ,∂∂xn).x...