1. The problem statement, all variables and given/known data I have to minimize the function (x1-1)2+x23+x1x2 by the steepest descent method. The initial point is [1,1]T 2. Relevant equations 3. The attempt at a solution The gradient of this function is ∇ƒ(x1,x2)=[2(x1-1)-x2 3x22-x1]. This gradient evaluated in the initial point is ∇ƒ(1,1)=[-1 2]. Following the steepest descent method it is mandatory to minimize the function ƒ(x0-α∇ƒ(x0)) in order to find the value of α. So ƒ(x0-α∇ƒ(x0))=-5α+15α2-8α3 and ƒ'(x0-α∇ƒ(x0))=-5+30α-24α2. This function has extreme points in α1=0.95061 and α2=5.094. In order to be a minimum of this curve ƒ''(x0-α∇ƒ(x0))=30-48α has to be positive. This is my problem ƒ''(x0-α∇ƒ(x0) evaluated at both α values is negative so they don´t minimize the direction. So what I am doing wrong?