Problem: Let $f,g : \mathbb{R} ^2 \to \mathbb{R} $ be defined by \[ f(x,y) = x^2 - \frac{3}{2}xy^2 \text{ and } g(x,y) = 4x^4 - 5x^2 y + y^2 \] for all $(x,y) \in \mathbb{R} ^2$.

Consider the following statements:

• P: $f$ has a saddle point at $(0,0)$.
• Q: $g$ has a saddle point at $(0,0)$.

Then

• both P and Q are TRUE
• P is FALSE but Q is TRUE
• P is TRUE but Q is FALSE
• both P and Q are FALSE