consider f (x, y, z)=x^2 + xy + yz + z^2 and x0=(1,1,1)^T. Computethe point x1 following x0 by the Newton minimization algorithm

consider f (x, y, z)=x^2 + xy + yz + z^2 and x0=(1,1,1)^T. Computethe point x1 following x0 by the Newton minimization algorithm

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x