Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Engineering Mathematics Calculus Maxima & Minima
Let 𝑓, 𝑔 ∶ ℝ2 → ℝ be defined by
𝑓(𝑥, 𝑦) = \(\rm x^2-\frac{3}{2}xy\) and 𝑔(𝑥, 𝑦) = 4𝑥4 − 5𝑥2𝑦 + 𝑦2
for all (𝑥, 𝑦) ∈ ℝ2 .
Consider the following statements:
𝑃: 𝑓 has a saddle point at (0,0).
𝑄: 𝑔 has a saddle point at (0,0).
Then
1
both 𝑃 and 𝑄 are TRUE
2
𝑃 is FALSE but 𝑄 is TRUE
3
𝑃 is TRUE but 𝑄 is FALSE
4
both 𝑃 and 𝑄 are FALSE
5
Question Not Attempted