I am given a function f(x_1, x_2) = -cos(x_1) * cos(x_2/5). I need to identify the region in which the Hessian matrix is positive definite. I know that the first term of the Hessian matrix has to be positive and so as its determinant. From these two inequalities I get:
cos(x_1) * cos(x_2/5) > 0 ------------(1)
cos^2(x_1) + cos^2(x_2/5) > 1 ----------(2)
I am not sure how to proceed to identify the region. Any idea?
Hessian is symmetric so you can then check Sylvester criterion.