Problem #2. Unconstrained optimization.
Consider the following ideal, convex function:
$f(x_1, x_2) = (x_1 - 2)^2 + 10 \cdot (x_2 - 3)^2$
1. Plot the contours of the function and its gradient.
2. Compute the point where $\nabla f(x) = 0$.
3. Solve the unconstrained optimization problem:
$\min_x f(x_1, x_2)$.
4. Verify $\nabla f(x) = 0$ at the optimal point.
