Consider the following function: $f(x, y) = 4x^2 + 2y^2 + 2xy - 4x + 6y$.
(a) Find the unique global minimiser $(x^*, y^*)$ of $f$.
(b) Starting at the point $(x_0, y_0) = (5, 2)$, how many iterations of the
steepest descent method would it take—at least—to guarantee that
the value of $q(x_n, y_n) := f(x_n, y_n) - f(x^*, y^*)$ is less than $10^{-8}$? Here
$(x_n, y_n)$ are the points obtained from the steepest descent method.