Exercises
The platform we use is Matlab.
1. Plot the following function $f(x,y) = x^3 + y^3 - 3x - 3y$ for the interval
$[-1.8, 1.8]$ and describe its features (minimum, maximum and saddle
point).
2. Find the stationary points of the function $f(x,y) = 8x^2 + 6y^2 - 2y^3 + 5$
and its function values.
3. Show that $f(x, y) = x^3 + y^3 - 3x - 2y$ defined on the convex set $\Omega =$
$\{(x, y): x > 0, y > 0\}$ is (strictly) convex. Find the global minimum.
