GATE XE (Engineering Sciences) 2025 - Question 19

Section: Engineering Mathematics | Marks: 2

Consider the function 𝑓(𝑥, 𝑦) = 𝑥2𝑦+ 2𝑥𝑦2 −2𝑥2𝑦2. Then which one of the following statements is correct ?

• A. ( 3 2 , 0) is a point of local maxima of 𝑓.
• B. (0, 3 4) is a point of local minima of 𝑓.
• C. ( 3 2 , 3 4) is a point of local maxima of 𝑓.
• D. ( 3 2 , 3 4) is a saddle point of 𝑓.

Answer: D. ( 3 2 , 3 4) is a saddle point of 𝑓.