F(x,y,z)=-2x^2,在x^2+y^2-2z^2=2的条件下的极大值

Question

F(x,y,z)=-2x^2,在x^2+y^2-2z^2=2的条件下的极大值

Answer 1

F(x,y,z) = -2x^2 = -2(2 + 2z^2 - y^2)
z = 0,
y = 10^n,n = 1,2,3,...,
x^2 = 2 - 10^n.
F(x,y,z) = -4 + 2*10^n
F(x,y,z)=-2x^2,在x^2+y^2-2z^2=2的条件下的极大值 does not exist.