Considere the following function $f$ defined by $$ f(x, y)=ln^2(y + x^2)+\sqrt{x}$$
Start at the point $(1, 0)$. Find the minimum of $f$ in the direction (line) $(1, 2)$ using the Golden-Section line-search algorithm with interval $[0, 1]$. Stop when the length of the interval is less than $0.15$. Note: the interval could be described by the parameter $t$, and a point along the direction $(1, 2)$ can be expressed as $(1, 0) + t(1, 2)$
In this case the function is a two variables function, how can I continue? Do I need a region for the values of $x$ and $y$? In a variable the idea is to extract regions depending on the product of the images of the points.