Let ( f(x,y) = x^2 + 3y^2 - \frac{2}{3} xy ) at ( (x,y) \in... | Mathematics | SolveeIt | Solveeit

Today, August 24

Question

Let $f(x,y) = x^2 + 3y^2 - \frac{2}{3} xy$ at $(x,y) \in \mathbb{R}^2$ . Then

A

$f$ has a point of local minimum

B

$f$ has a point of local maximum

C

$f$ has a saddle point

D

$f$ has no point of local minimum, no point of local maximum, and no saddle point

Answer

$f$ has a saddle point

Explanation

Solution

The correct option is (C): $f$ has a saddle point